To see the other types of publications on this topic, follow the link: Automorphisms.
Dissertations / Theses on the topic 'Automorphisms'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 dissertations / theses for your research on the topic 'Automorphisms.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Sutherland, David C. (David Craig). "Automorphism Groups of Strong Bruhat Orders of Coxeter Groups." Thesis, North Texas State University, 1986. https://digital.library.unt.edu/ark:/67531/metadc330906/.
Full textAbstract:
In this dissertation, we describe the automorphism groups for the strong Bruhat orders A_n-1, B_n, and D_n. In particular, the automorphism group of A_n-1 for n ≥ 3 is isomorphic to the dihedral group of order eight, D_4; the automorphism group of B_n for n ≥ 3 is isomorphic to C_2 x C_2 where C_2 is the cyclic group of order two; the automorphism group of D_n for n > 5 and n even is isomorphic to C_2 x C_2 x C_2; and the automorphism group of D_n for n ≥ 5 and n odd is isomorphic to the dihedral group D_4.
2
Davies, D. H. "Automorphisms of designs." Thesis, University of East Anglia, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.304043.
Full text
3
Karlsson, Jesper. "Symplectic Automorphisms of C2n." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-144390.
Full textAbstract:
This essay is a detailed survey of an article from 1996 published by Franc Forstneric, where he studies symplectic automorphisms of C2n. The vision is to introduce the density property for holomorphic symplectic manifolds. Our idea is that of Dror Varolin when he in 2001 introduced the concept of density property for Stein manifolds. The main result here is the introduction of symplectic shears on C2n equipped with a holomorphic symplectic form and to show that the group generated by finite compositions of symplectic shears is dense in the group of symplectic automorphisms of C2n in the compact-open topology. We give a complete background of the tools from the theory of ordinary differential equations, smooth manifolds, and complex and symplectic geometry that is needed in order to prove this result.Den här uppsatsen är en detaljerad undersökning av en artikel från 1996 publicerad av Franc Forstneric där han studerar symplektiska automorfismer av C2n. Visionen är att introducera täthetsegenskapen för holomorfa symplektiska mångfalder. Våran idé är som den av Dror Varolin när han 2001 introducerade täthetsegenskapen för Stein mångfalder. Huvudresultatet här är införandet av symplektiska skjuvningar på C2n med en holomorfisk symplektisk form och att visa att gruppen som genereras av ändliga sammansättningar av symplektiska skjuvningar är tät i gruppen av symplektiska automorfismer av C2n i den kompakt-öppna topologin. Vi ger en fullständig bakgrund av de verktyg från teorin om ordinära differentialekvationer, släta mångfalder och komplex och symplektisk geometri som behövs för att visa detta.
4
CARVALHO, LEONARDO NAVARRO DE. "GENERIC AUTOMORPHISMS OF HANDLEBODIES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2002. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=3970@1.
Full textAbstract:
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOAutomorfismos genéricos de cubos com alças (handlebodies) aparecem do estudo de classes the isotopia de automorfismos de variedades orientáveis de dimensão três. Automorfismos genéricos permanecem como uma das partes menos entendidas desse estudo.Dado um automorfismo genérico de um cubo com alças, é conhecida uma forma de se construir uma laminação bidimensional que é invariante pelo automorfismo. A essa laminação se associa um fator de crescimento. É sabido que, no caso de tal fator de crescimento ser minimal - uma característica importante, pois mede a complexidade essencial do automorfismo - a laminação deve gozar de uma certa propriedade de incompressibilidade. Nessa tese mostramos que o processo de se achar uma laminação com tal propriedade é algoritmico. Por outro lado, mostramos que tal propriedade não garante que o respectivo fator de crescimento seja minimal. Propomos uma outra propriedade, tensão transversal, mais forte que incompressibilidade, que conjecturamos também ser condição necessária para que o fator de crescimento seja minimal. Provamos a conjectura em alguns casos.Além dos resultados mencionados acima, desenvolvemos métodos para gerar automorfismos genéricos de cubos com alcas, que usamos para apresentar alguma variedade de exemplos.
Generic automorphisms of handlebodies appear naturally in the study of isotopy classes of automophisms of orientable three-dimensional manifolds. Generic automorphisms remain as one of the least understood parts of this study. Given a generic automorphism of a handlebody one can construct a bidimensional lamination that is invariant under the automorphism. There is a growth rate associated to this lamination. It is known that, when this growth rate is minimal among all possible choices (an important property, for it measures the essential complexity of the automorphism), the lamination must have a certain incompressibility property. On this thesis we show that the process of
5
Grossi, Annalisa <1992>. "Automorphisms of O'Grady's sixfolds." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amsdottorato.unibo.it/9441/1/Tesi%20Dottorato.pdf.
Full textAbstract:
We study automorphisms of irreducible holomorphic symplectic (IHS) manifolds deformation equivalent to the O’Grady’s sixfold. We classify non-symplectic and symplectic automorphisms using lattice theoretic criterions related to the lattice structure of the second integral cohomology. Moreover we introduce the concept of induced automorphisms. There are two birational models for O'Grady's sixfolds, the first one introduced by O'Grady, which is the resolution of singularities of the Albanese fiber of a moduli space of sheaves on an abelian surface, the second one which concerns in the quotient of an Hilbert cube by a symplectic involution. We find criterions to know when an automorphism is induced with respect to these two different models, i.e. it comes from an automorphism of the abelian surface or of the Hilbert cube.
6
Bonfanti, M. A. "ALGEBRAIC SURFACES WITH AUTOMORPHISMS." Doctoral thesis, Università degli Studi di Milano, 2015. http://hdl.handle.net/2434/345557.
Full textAbstract:
In my thesis I worked on two different projects, both related with projective surfaces with automorphisms. In the first one I studied Abelian surfaces with an automorphism and quaternionic multiplication: this work has already been accepted for publication in the Canadian Journal of Mathematics. In the second project I treat surfaces isogenous to a product of curves and their cohomology.
Abelian Surfaces with an Automorphism
The Abelian surfaces, with a polarization of a fixed type, whose endomorphism ring is an order in a quaternion algebra are parametrized by a curve, called Shimura curve, in the moduli space of polarized Abelian surfaces. There have been several attempts to find concrete examples of such Shimura curves and of the Abelian surfaces over this curve. In [HM95] Hashimoto and Murabayashi find Shimura curves as the intersection, in the moduli space of principally polarized Abelian surfaces, of Humbert surfaces. Such Humbert surfaces are now known “explicitly” in many other cases and this might allow one to find explicit models of other Shimura curves. Other approaches are taken in [Elk08] and [PS11].
We consider the rather special case where one of the Abelian surfaces in the family is the selfproduct of an elliptic curve. We assume this elliptic curve to have an automorphism of order three or four. For a fixed product polarization of type (1, d), we denote by Hj,d the set of the deformations of the selfproduct with the automorphism of order j. We prove the following theorem:
Theorem. Let j ∈ {3,4}, d ∈ Z, d > 0 and let τ ∈ Hj,d, so that the Abelian surface Aτ,d has an automorphism φj of order j. Then the endomorphism algebra of Aτ,d also contains an element ψj with ψj^2 = d. Moreover, for a general τ ∈ Hj,d one has
End(Aτ,d)Q =(−j,d)/Q
where (a, b)/Q := Q1 ⊕ Qi ⊕ Qj ⊕ Qk is the quaternion algebra with i^2 = a, j^2 =b and ij=−ji.
It is easy compute for which d the quaternion algebra (−j,d)/Q is a skew field: for these d the general Abelian surface in the family Hj,d is simple. In particular this provides examples of simple Abelian surfaces with an automorphism of order three and four. This construction, together with well-known results about automorphisms of Abelian surfaces (see [BL04, Chapter 13]), leads to:
Theorem. Let A be a simple Abelian surface and φ ∈ Aut(A) a non-trivial automorphism of finite order. Then ord(φ) ∈ {3, 4, 5, 6, 10}.
We focus in particular on the family H3,2 of Abelian surfaces with an automorphism of order three and a polarization of type (1,2). In [Bar87] Barth provides a description of a moduli space M2,4, embedded in P5, of (2, 4)-polarized Abelian surfaces with a level structure. Since the polarized Abelian surfaces we consider have an automorphism of order three, the corresponding points in M2,4 are fixed by an automorphism of order three of P^5. This allows us to explicitly identify the Shimura curve in M2,4 that parametrizes the Abelian surfaces with quaternionic multiplication by the
maximal order O6 in the quaternion algebra with discriminant 6. It is embedded as a line in M2,4 ⊂ P5 and the symmetric group S4 acts on this line by changing the level structures. According to Rotger [Rot04], an Abelian surface with endomorphism ring O6 is the Jacobian of a unique genus two curve. We show explicitly how to find such genus two curves, or rather their images in the Kummer surface embedded in P5 with a (2,4)-polarization.
These curves were already been considered by Hashimoto and Murabayashi in [HM95]: we give the explicit relation between their description and ours. Moreover we find a Humbert surface in M2,4 that parametrizes Abelian surfaces with Z( 2) in the endomorphism ring.
Cohomology of surfaces isogenous to a product
Surfaces isogenous to a product of curves provide examples of surfaces of general type with many different geometrical invariants. They have been introduced by Catanese in [Cat00]:
Definition. A smooth surface S is said to be isogenous to a product (of curves) if it is isomorphic to a quotient (C×D)/G where C and D are curves of genus at least one and G is a finite group acting freely on C × D.
We say that a surface isogenous to a product is of mixed type if there exists a element of G interchanging the two curves; otherwise, if G acts diagonally on the product, we say that the surface is of unmixed type. A surface isogenous to a product is of general type if the genus of both curves, C and D, is greater or equal to 2: in this case we say that the surface is isogenous to a higher product.
The cohomology groups of a surface S = (C × D)/G isogenous to a product of unmixed type are determined by the action of the group G on the cohomology groups of the curves. Moreover the action of an automorphism group G on a smooth curve C forces a decomposition of the first cohomology group, as described in [BL04, section 13.6] and in [Roj07]:
Proposition (Group algebra decomposition). Let G be a finite group acting on a curve C. Let W1, ..., Wr denote the irreducible rational representations of G and let ni := dimDi (Wi), with Di := EndG(Wi), for i = 1, ..., r. Then there are rational Hodge substructures B1, ..., Br such that
H1(C, Q) ≃ n1B1+...+nrBr.
From this a decomposition of the cohomology groups of the surface S follows directly. We apply these results to surfaces isogenous to a higher product of unmixed type with χ(OS) = 2 and q(S) = 0: they have been studied and classified by Gleissner in [Gle13]. For these surfaces the Hodge diamond is fixed and in particular the Hodge numbers of the second coho- mology groups are the same as those of an Abelian surface.
From Gleissner’s classification we obtain a complete list of the 21 possible groups G. We proved that the second cohomology group of these surfaces can be described explicitly as follows:
Theorem. Let S be a surface isogenous to a higher product of unmixed type with χ(OS) = 2, q(S) = 0. Then there exist two elliptic curves E1 and E2 such that H2(S, Q) ∼= H2(E1 × E2, Q) as rational Hodge structures.
In general it is not possible to construct these elliptic curves “geometrically” using the action of G. More precisely there are no intermediate coverings πF : C → C/F and πH : D → D/H, F, H ≤ G with C/F = E1 and D/H = E2: we can only prove that such elliptic curves must exist. The proof of the theorem is standard for all but four groups: in these cases we study one by one the corresponding surfaces in order to construct the elliptic curves. As a further application we use this approach to study some surfaces isogenous to a higher product with pg = q = 2, in particular those are of Albanese general type.
7
Fullarton, Neil James. "Palindromic automorphisms of free groups and rigidity of automorphism groups of right-angled Artin groups." Thesis, University of Glasgow, 2014. http://theses.gla.ac.uk/5323/.
Full textAbstract:
Let F_n denote the free group of rank n with free basis X. The palindromic automorphism group PiA_n of F_n consists of automorphisms taking each member of X to a palindrome: that is, a word on X that reads the same backwards as forwards. We obtain finite generating sets for certain stabiliser subgroups of PiA_n. We use these generating sets to find an infinite generating set for the so-called palindromic Torelli group PI_n, the subgroup of PiA_n consisting of palindromic automorphisms inducing the identity on the abelianisation of F_n. Two crucial tools for finding this generating set are a new simplicial complex, the so-called complex of partial pi-bases, on which PiA_n acts, and a Birman exact sequence for PiA_n, which allows us to induct on n. We also obtain a rigidity result for automorphism groups of right-angled Artin groups. Let G be a finite simplicial graph, defining the right-angled Artin group A_G. We show that as A_G ranges over all right-angled Artin groups, the order of Out(Aut(A_G)) does not have a uniform upper bound. This is in contrast with extremal cases when A_G is free or free abelian: in these cases, |Out(Aut(A_G))| < 5. We prove that no uniform upper bound exists in general by placing constraints on the graph G that yield tractable decompositions of Aut(A_G). These decompositions allow us to construct explicit members of Out(Aut(A_G)).
8
Tabbaa, Dima al. "On the classification of some automorphisms of K3 surfaces." Thesis, Poitiers, 2015. http://www.theses.fr/2015POIT2299/document.
Full textAbstract:
Un automorphisme non-symplectique d'ordre fini n sur une surface X de type K3 est un automorphisme σ ∈ Aut(X) qui satisfait σ*(ω) = λω où λ est une racine primitive n-ième de l'unité et ω est le générateur de H2,0(X). Dans cette thèse on s’intéresse aux automorphismes non-symplectiques d'ordre 8 et 16 sur les surfaces K3. Dans un premier temps, nous classifionsles automorphismes non-symplectiques σ d'ordre 8 quand le lieu fixe de sa quatrième puissance σ⁴ contient une courbe de genre positif, on montre plus précisément que le genre de la courbe fixée par σ est au plus un. Ensuite nous étudions le cas où le lieu fixe de σ contient au moins une courbe et toutes les courbes fixées par sa quatrième puissance σ⁴ sont rationnelles. Enfin nous étudions le cas où σ et son carré σ² agissent trivialement sur le groupe de Néron-Severi. Nous classifions toutes les possibilités pour le lieu fixe de σ et de son carré σ² dans ces trois cas. Nous obtenons la classification complète pour les automorphismes non-symplectiques d'ordre 8 sur les surfaces K3. Dans la deuxième partie de la thèse, nous classifions les surfaces K3 avec automorphisme non-symplectique d'ordre 16 en toute généralité. Nous montrons que le lieu fixe contient seulement courbes rationnelles et points isolés et nous classifions complètement les sept configurations possibles. Si le groupe de Néron-Severi a rang 6, alors il y a deux possibilités et si son rang est 14, il y a cinq possibilités. En particulier si l'action de l'automorphisme est trivial sur le groupe de Néron-Severi, alors nous montrons que son rang est six. Enfin, nous construisons des exemples qui correspondent à plusieurs cas dans la classification des automorphismes non-symplectiques d'ordre 8 et nous donnons des exemples pour chaque cas dans la classification des automorphismes non-symplectiques d'ordre 16A non-symplectic automorphism of finite order n on a K3 surface X is an automorphism σ ∈ Aut(X) that satisfies σ*(ω) = λω where λ is a primitive n−root of the unity and ω is a generator of H2,0(X). In this thesis we study the non-symplectic automorphisms of order 8 and 16 on K3 surfaces. First we classify the non-symplectic automorphisms σ of order eight when the fixed locus of its fourth power σ⁴ contains a curve of positive genus, we show more precisely that the genus of the fixed curve by σ is at most one. Then we study the case of the fixed locus of σ that contains at least a curve and all the curves fixed by its fourth power σ⁴ are rational. Finally we study the case when σ and its square σ² act trivially on the Néron-Severi group. We classify all the possibilities for the fixed locus of σ and σ² in these three cases. We obtain a complete classifiction for the non-symplectic automorphisms of order 8 on a K3 surfaces.In the second part of the thesis, we classify K3 surfaces with non-symplectic automorphism of order 16 in full generality. We show that the fixed locus contains only rational curves and isolated points and we completely classify the seven possible configurations. If the Néron-Severi group has rank 6, there are two possibilities and if its rank is 14, there are five possibilities. In particular ifthe action of the automorphism is trivial on the Néron-Severi group, then we show that its rank is six.Finally, we construct several examples corresponding to several cases in the classification of the non-symplectic automorphisms of order 8 and we give an example for each case in the classification of the non-symplectic automorphisms of order 16
9
Sebille, Michel. "Design :construction, automorphisms and colourings." Doctoral thesis, Universite Libre de Bruxelles, 2002. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211428.
Full text
10
Bidwell, Jonni, and n/a. "Computing automorphisms of finite groups." University of Otago. Department of Mathematics & Statistics, 2007. http://adt.otago.ac.nz./public/adt-NZDU20070320.162909.
Full textAbstract:
In this thesis we explore the problem of computing automorphisms of finite groups, eventually focusing on some group product constructions. Roughly speaking, the automorphism group of a group gives the nature of its internal symmetry. In general, determination of the automorphism group requires significant computational effort and it is advantageous to find situations in which this may be reduced.
The two main results give descriptions of the automorphism groups of finite direct products and split metacyclic p-groups. Given a direct product G = H x K where H and K have no common direct factor, we give the order and structure of Aut G in terms of Aut H, Aut K and the central homomorphism groups Hom (H, Z(K)) and Hom (K, Z(H)). A similar result is given for the the split metacyclic p-group, in the case where p is odd. Implementations of both of these results are given as functions for the computational algebra system GAP, which we use extensively throughout.
An account of the literature and relevant standard results on automorphisms is given. In particular we mention one of the more esoteric constructions, the automorphism tower. This is defined as the series obtained by repeatedly taking the automorphism group of some starting group G₀. There is interest as to whether or not this series terminates, in the sense that some group is reached that is isomorphic to its group of automorphisms. Besides a famous result of Wielandt in 1939, there has not been much further insight gained here. We make use of the technology to construct several examples, demonstrating their complex and varied behaviour.
For the main results we introduce a 2 x 2 matrix description for the relevant automorphism groups, where the entries come from the homorphism groups mentioned previously. In the case of the direct product, this is later generalised to an n x n matrix (when we consider groups with any number of direct factors) and the common direct factor restriction is relaxed to the component groups not having a common abelian direct factor. In the case of the split metacyclic p-group, our matrices have entries that are not all homomorphisms, but are similar. We include the code for our GAP impementation of these results, which we show significantly expedites computation of the automorphism groups.
We show that this matrix language can be used to describe automorphisms of any semidirect product and certain central products too, although these general cases are much more complicated. Specifically, multiplication is no longer defined in such a natural way as is seen in the previous cases and the matrix entries are mappings much less well-behaved than homomorphisms. We conclude with some suggestion of types of semidirect products for which our approach may yield a convenient description of the automorphisms.
11
Kestner, Charlotte Hastings. "Measurability, modules and generic automorphisms." Thesis, University of Leeds, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.578647.
Full textAbstract:
Originally developed [17] as a generalization of dimension and measure on pseudofinite fields, MS-measurability is a relatively new concept in model theory. We look at MS-measurability in structures which already have a well-understood model theory. We also consider other notions of rank within these structures. Firstly, we show that for any module it suffices to put an MS-measuring function on the positive primitive subgroups for the whole structure to be MS-measurable. We give a precise classification of w-stable Abelian groups in terms of MS-measurability. We also show that in this context MS-measurability is compatible with a R[t]-valued measure. Secondly, we look at MS-measurability in the context of strongly minimal structures. We show that MS-measurability is equivalent to uni- modularity. We also consider the definable multiplicity property. We show that it is incomparable to MS-measurability. We give an example of a finite Morley rank structure without the definable multiplicity property for which we conjecture all strongly minimal definable sets have the definable multiplicity property. Finally, we examine structures with a generic automorphism. We show that if T is an w-stable Abelian group then T A is w-stable if and only if T is MS-measurable. We also give a Morley rank two example in which rank in the fixed field behaves unlike rank in the fixed field of a strongly minimal theory with a generic automorphism
12
Webb, B. S. "Automorphisms of finite incidence structures." Thesis, University of East Anglia, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.306212.
Full text
13
Myhill, Richard Graham. "Automorphisms and twisted vertex operators." Thesis, Durham University, 1987. http://etheses.dur.ac.uk/6674/.
Full textAbstract:
This work is an examination of various aspects of twisted vertex operator representations of Kac-Moody algebras. It starts with an introduction to Kac-Moody algebras and string theories, including a discussion of the propagation of strings on orbifolds. String interactions in a subclass of such models naturally involve twisted vertex operators. The centrally extended loop algebra realization of Kac-Moody algebras is used to explain why the inequivalent gradations of basic representations of Kac-Moody algebras g(^r) associated with g are in one-to-one correspondence with the conjugacy classes of the automorphism group of the root system, aut Ф(_g).The structure of the automorphism groups of the simple Lie algebra root systems are examined. A method of classifying the conjugacy classes of the Weyl groups is explained and then extended to cover the whole automorphism group in cases where there are additional Dynkin diagram symmetries. All possible automorphisms, a, that have the property that det (1 – σ(^r)) ≠ 0, r = 1, ….. , n - 1 where n is the order of a, are determined. Such automorphisms lead to interesting orbifold models in which some of the calculations are simplified. A thorough exposition of the twisted vertex operator representation is given including a detailed explanation of the zero-mode Hilbert space and the construction of the required cocycle operators. The relation of the vacuum degeneracy to the number of fixed subspace singularities in the orbifold construction is discussed. Explicit examples of twisted vertex operators and their associated cocycles are given. Finally it is shown how the twisted and an alternative shifted vertex operator representation of the same gradation may be identified. This is used to determine the invariant subalgebras of the gradations along with the vacuum degeneracies and conformal weights of the representations. The results of calculations for inequivalent gradations of the simply laced exceptional algebras are given.
14
Brown, Christian. "Petit algebras and their automorphisms." Thesis, University of Nottingham, 2018. http://eprints.nottingham.ac.uk/49613/.
Full text
15
Matthews, David. "Automorphisms of random recursive trees." Thesis, University of Southampton, 2017. https://eprints.soton.ac.uk/415900/.
Full text
16
Lind, Andreas. "Holomorphic automorphisms of Danielewski surfaces." Doctoral thesis, Sundsvall : Dep. of Natural Sciences, Engineering and Mathematics, Mid Sweden University, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-10360.
Full text
17
DOSE, VALERIO. "Modular Curves and their Automorphisms." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2015. http://hdl.handle.net/2108/202163.
Full text
18
Aurand, Eric William. "Infinite Planar Graphs." Thesis, University of North Texas, 2000. https://digital.library.unt.edu/ark:/67531/metadc2545/.
Full textAbstract:
How many equivalence classes of geodesic rays does a graph contain? How many bounded automorphisms does a planar graph have? Neimayer and Watkins studied these two questions and answered them for a certain class of graphs.
Using the concept of excess of a vertex, the class of graphs that Neimayer and Watkins studied are extended to include graphs with positive excess at each vertex. The results of this paper show that there are an uncountable number of geodesic fibers for graphs in this extended class and that for any graph in this extended class the only bounded automorphism is the identity automorphism.
19
Perepechko, Aleksandr. "Automorphismes des variétés affines." Thesis, Grenoble, 2013. http://www.theses.fr/2013GRENM065/document.
Full textAbstract:
La thèse se compose de deux parties. La première partie est consacrée aux transformations des algèbres de dimension finie. Il est facile de voir que le groupe d'automorphismes d'une algèbre de dimension finie est un groupe algébrique affine. N.L. Gordeev et V.L. Popov ont démontré que n'importe quel groupe algébrique affine est isomorphe au groupe d'automorphismes de l'algèbre de dimension finie. Utilisant l'approche similaire nous démontrons que tout monoïde affine peut être obtenue comme un monoïde des endomorphismes d'une algèbre de dimension finie. Ensuite, nous étudions la solvabilité des groupes d'automorphismes d'algèbres commutatives de dimension finie. Nous introduisons un critère de leur solvabilité et l'appliquons aux intersections complètes et aux singularités isolées d'hypersurfaces. Nous étudions également les cas extrêmes du critère introduit. La deuxième partie de la thèse est consacrée à la transitivité infinie de groupes d'automorphismes spéciales de variétés affines et quasi-affines. Cette propriété est équivalente à la flexibilité pour les variétés affines. Tout d'abord, nous montrons l'équivalence entre la transitivité et la transitivité infinie des groupes d'automorphismes spéciaux sur un corps algébriquement clos de caractéristique arbitraire. Nous fournissons ensuite le critère de la flexibilité pour les cônes affines sur les variétés projectives et nous l'appliquons aux surfaces del Pezzo de degré 4 et 5. Enfin, nous étudions la flexibilité des torseurs universels sur les variétés couvertes par des espaces affines et fournissons une large gamme de familles de variétés flexiblesThe thesis consists of two parts. The first part is dedicated to transformations of finite-dimensional algebras. It is easy to see that the automorphism group of a finite-dimensional algebra is an affine algebraic group. N.L.~Gordeev and V.L.~Popov proved that any affine algebraic group is isomorphic to the automorphism group of some finite-dimensional algebra. We use a similar approach to prove that any affine algebraic monoid can be obtained as the endomorphisms' monoid of a finite-dimensional algebra. Next, we study the solvability of automorphism groups of commutative Artin algebras. We introduce a criterion of their solvability and apply it to complete intersections and to isolated hypersurface singularities. We also study extremal cases of the introduced criterion. The second part of the thesis is dedicated to the infinite transitivity of special automorphism groups of affine and quasiaffine varieties. This property is equivalent to the flexibility for affine varieties. Firstly, we prove the equivalence of transitivity and infinite transitivity of special automorphism groups over algebraically closed field of arbitrary characteristic. Then we provide the criterion of flexibility for affine cones over projective varieties and apply it to del Pezzo surfaces of degree 4 and 5. Finally, we study flexibility of universal torsors over varieties covered by affine spaces and provide a wide range of families of flexible varieties
20
Popov, Vladimir L., and popov@ppc msk ru. "On Polynomial Automorphisms of Affine Spaces." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi938.ps.
Full text
21
Wermer, Markus-Ludwig [Verfasser]. "Automorphisms of buildings / Markus-Ludwig Wermer." Gießen : Universitätsbibliothek, 2015. http://d-nb.info/1077438818/34.
Full text
22
Griffin, James Thomas. "Automorphisms of free products of groups." Thesis, University of Cambridge, 2013. https://www.repository.cam.ac.uk/handle/1810/244265.
Full textAbstract:
The symmetric automorphism group of a free product is a group rich in algebraic structure and with strong links to geometric configuration spaces. In this thesis I describe in detail and for the first time the (co)homology of the symmetric automorphism groups. To this end I construct a classifying space for the Fouxe-Rabinovitch automorphism group, a large normal subgroup of the symmetric automorphism group. This classifying space is a moduli space of 'cactus products', each of which has the homotopy type of a wedge product of spaces. To study this space we build a combinatorial theory centred around 'diagonal complexes' which may be of independent interest. The diagonal complex associated to the cactus products consists of the set of forest posets, which in turn characterise the homology of the moduli spaces of cactus products. The machinery of diagonal complexes is then turned towards the symmetric automorphism groups of a graph product of groups. I also show that symmetric automorphisms may be determined by their categorical properties and that they are in particular characteristic of the free product functor. This goes some way to explain their occurence in a range of situations. The final chapter is devoted to a class of configuration spaces of Euclidean n-spheres embedded disjointly in (n+2)-space. When n = 1 this is the configuration space of unknotted, unlinked loops in 3-space, which has been well studied. We continue this work for higher n and find that the fundamental groups remain unchanged. We then consider the homology and the higher homotopy groups of the configuration spaces. Our last contribution is an epilogue which discusses the place of these groups in the wider field of mathematics. It is the functoriality which is important here and using this new-found emphasis we argue that there should exist a generalised version of the material from the final chapter which would apply to a far wider range of configuration spaces.
23
Laurence, Michael Rupen. "Automorphisms of graph products of groups." Thesis, Queen Mary, University of London, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.412581.
Full textAbstract:
Let r be a graph with vertex set V and for every v E V let Gv be a group with present ation (Sv I Rv). Let E ~ V X V be the set of pairs of adj acent vertices. Then we define the group G = Gr to be the group with presentation G = (SvVv E VI R; Vv E V, [Sv, SVI] = 1 iff (v,v') E E). In [2, LEMMA 3.3] it is shown that up to isomorphism G is independent of the choice of presentation of each group Gv. We call the group G a graph product of groups. Graph products include as special cases free products and direct products, corresponding to the graph G being dixcrete and complete respectively. If the vertex groups G; are infinite cyclic then G is called a graph group and we identify each vertex v with a fixed generator of the vertex group Gv• There is a normal form theorem for graph products which is a generalisation of the normal form theorem for free products and which was proved in [2]. In Part 1we give an alternative proof. We then move on to the study of automorphisms of graph products. In full generality this is an impossible task; however some progress can be made in certain special cases. We first consider the case where G is a graph group. Servatius in [1] gave a simple set of elements of Aut( G), which he calls elementary automorphisms, and proved that if certain conditions are imposed on the graph r then the elementary automorphisms generate Aut(G). In Part 2 we will prove that this holds for all finite graphs r. In Part 3 we study Aut( G) in the case where each vertex group Gv is cyclic of order p for some fixed prime p and we find a simple set of generators for Aut(G). In the case p = 2 we also obtain a presentation for Aut( G). In this case G is a right-angled Coxeter group
24
Saleh, Ibrahim A. "Cluster automorphisms and hyperbolic cluster algebras." Diss., Kansas State University, 2012. http://hdl.handle.net/2097/14195.
Full textAbstract:
Doctor of PhilosophyDepartment of Mathematics
Zongzhu Lin
Let A[subscript]n(S) be a coefficient free commutative cluster algebra over a field K. A cluster automorphism is an element of Aut.[subscript]KK(t[subscript]1,[dot, dot, dot],t[subscript]n) which leaves the set of all cluster variables, [chi][subscript]s invariant. In Chapter 2, the group of all such automorphisms is studied in terms of the orbits of the symmetric group action on the set of all seeds of the field K(t[subscript]1,[dot,dot, dot],t[subscript]n). In Chapter 3, we set up for a new class of non-commutative algebras that carry a non-commutative cluster structure. This structure is related naturally to some hyperbolic algebras such as, Weyl Algebras, classical and quantized universal enveloping algebras of sl[subscript]2 and the quantum coordinate algebra of SL(2). The cluster structure gives rise to some combinatorial data, called cluster strings, which are used to introduce a class of representations of Weyl algebras. Irreducible and indecomposable representations are also introduced from the same data. The last section of Chapter 3 is devoted to introduce a class of categories that carry a hyperbolic cluster structure. Examples of these categories are the categories of representations of certain algebras such as Weyl algebras, the coordinate algebra of the Lie algebra sl[subscript]2, and the quantum coordinate algebra of SL(2).
25
Toinet, Emmanuel. "Automorphisms of right-angled Artin groups." Thesis, Dijon, 2012. http://www.theses.fr/2012DIJOS003.
Full textAbstract:
Cette thèse a pour objet l’étude des automorphismes des groupes d’Artin à angles droits. Etant donné un graphe simple fini G, le groupe d’Artin à angles droits GG associé à G est le groupe défini par la présentation dont les générateurs sont les sommets de G, et dont les relateurs sont les commutateurs [v,w], où {v,w} est une paire de sommets adjacents. Le premier chapitre est conçu comme une introduction générale à la théorie des groupes d’Artin à angles droits et de leurs automorphismes. Dans un deuxième chapitre, on démontre que tout sous-groupe sous-normal d’indice une puissance de p d’un groupe d’Artin à angles droits est résiduellement p-séparable. Comme application de ce résultat, on montre que tout groupe d’Artin à angles droits est résiduellement séparable dans la classe des groupes nilpotents sans torsion. Une autre application de ce résultat est que le groupe des automorphismes extérieurs d’un groupe d’Artin à angles droits est virtuellement résiduellement p-fini. On montre également que le groupe de Torelli d’un groupe d’Artin à angles droits est résiduellement nilpotent sans torsion, et, par suite, résiduellement p-fini et bi-ordonnable. Dans un troisième chapitre, on établit une présentation du sous-groupe Conj(GG) deAut(GG) formé des automorphismes qui envoient chaque générateur sur un conjugué de lui-mêmeThe purpose of this thesis is to study the automorphisms of right-angled Artin groups. Given a finite simplicial graph G, the right-angled Artin group GG associated to G is the group defined by the presentation whose generators are the vertices of G, and whose relators are commuta-tors of pairs of adjacent vertices. The first chapter is intended as a general introduction to the theory of right-angled Artin groups and their automor-phisms. In a second chapter, we prove that every subnormal subgroup ofp-power index in a right-angled Artin group is conjugacy p-separable. As an application, we prove that every right-angled Artin group is conjugacy separable in the class of torsion-free nilpotent groups. As another applica-tion, we prove that the outer automorphism group of a right-angled Artin group is virtually residually p-finite. We also prove that the Torelli group ofa right-angled Artin group is residually torsion-free nilpotent, hence residu-ally p-finite and bi-orderable. In a third chapter, we give a presentation of the subgroup Conj(GG) of Aut(GG) consisting of the automorphisms thats end each generator to a conjugate of itself
26
Praggastis, Brenda L. "Markov partitions for hyperbolic toral automorphisms /." Thesis, Connect to this title online; UW restricted, 1992. http://hdl.handle.net/1773/5773.
Full text
27
Lee, Kyung Il. "Automorphisms and linearisations of computable orderings." Thesis, University of Leeds, 2011. http://etheses.whiterose.ac.uk/2166/.
Full textAbstract:
In this thesis, we study computable content of existing classical theorems on linearisations of partial orderings and automorphisms of linear orderings, and provide computational refinements in terms of the Ershov hierarchy. In Chapter 2, we examine questions as to the constructiveness of linearisations obtained in terms of the Ershov hierarchy, while respecting particular constraints. The main result here entails a proof that every computably well-founded computable partial ordering has a computably well-founded ω-c.e. linear extension. In Chapter 3, we examine questions as to how less constructive rigidities of certain order types break down within the context of the Ershov hierarchy, and introduce uniform Δ02 classes as likely candidates in the case of order types 2.η and ω + ς.
28
Nguyen, Aude. "Constructions and automorphisms of Kac-Moody groups." Doctoral thesis, Universite Libre de Bruxelles, 2010. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210072.
Full textAbstract:
Les travaux de Killing et Cartan ont montré la correspondance entre les algèbres de Lie semi-simples complexes et les matrices de Cartan. Ces dernières sont des matrices sur les entiers satisfaisants certaines propriétés, parmi lesquelles une condition de positivité. Si cette condition est omise, on obtient une matrice de Cartan généralisée. On peut y étendre la présentation de Serre pour les algèbre de Lie semi-simples et obtenir les algèbres de Kac-Moody. L'intérêt de l'étude des algèbres de Lie semi-simples réside dans le fait qu'elles induisent la plupart des groupes simples finis, comme le montre la construction de Chevalley. Il se fait que cette construction se généralise aux algèbres de Kac-Moody.
L'ingrédient principal de cette construction est l'utilisation d'un système de sous-groupes dans un groupe de Kac-Moody, ceux-ci étant indicés par les racines du système de Coxeter associé à la matrice de Cartan généralisée. Tits a réalisé l'axiomatique de ce système de sous-groupes, une donnée radicielle jumelée, pour un système de Coxeter quelconque. Par définition, les groupes de Kac-Moody sur un corps commutatif admettent une donnée radicielle jumelée.
En réalité les notions de donnée radicielle jumelée et d'immeuble jumelé de Moufang sont essentiellement équivalentes.
Au vu de la classification des immeubles sphériques et des polygones de Moufang, on obtient une classification complète des données radicielles sphériques irréductibles de rang au moins 2. Il se trouve qu'elles sont toutes d'origine algébrique (i.e. obtenues par constructions algébriques à partir de groupes de Chevalley).
Dans le cas sphérique, la situation est différente. D'une part, des résultats de Mühlherr semblent indiquer que les données radicielles jumelées 2-sphériques seraient d'origine algébrique. D'autre part Rémy et Ronan ont construit des exemples exotiques à angles droits pour lesquels l'adjectif "d'origine algébrique" est inapproprié.
Néanmoins ces exemples sont toujours relativement proches d'une construction algébrique. On ne peut donc rien conclure sur les données radicielles jumelées. Afin de répondre à cette question, on peut essayer de prouver des théorèmes structurels sur les données radicielles jumelées ou en donner des constructions permettant plus de flexibilité.
Les principaux résultats de cette thèse sont motivés par ces lignes directrices:
- nous prouvons un critère d'existence général pour les données radicielles jumelées;
- nous donnons une réponse affirmative à une question sur les automorphismes des groupes de Kac-Moody laissée ouverte dans un article de Caprace;
- nous proposons une définition d'une donnée radicielle jumelée sur un corps commutatif de caractéristique p.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
29
Brewis, Louis Hugo. "Automorphisms of curves and the lifting conjecture." Thesis, Link to the online version, 2005. http://hdl.handle.net/10019/1050.
Full text
30
Joumaah, Malek [Verfasser]. "Automorphisms of irreducible symplectic manifolds / Malek Joumaah." Hannover : Technische Informationsbibliothek und Universitätsbibliothek Hannover (TIB), 2015. http://d-nb.info/1068920580/34.
Full text
31
Schlemmer, Tobias. "Annotating Lattice Orbifolds with Minimal Acting Automorphisms." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-96517.
Full textAbstract:
Context and lattice orbifolds have been discussed by M. Zickwolff, B. Ganter and D. Borchmann. Preordering the folding automorphisms by set inclusion of their orbits gives rise to further development. The minimal elements of this preorder have a prime group order and any group element can be dissolved into the product of group elements whose group order is a prime power. This contribution describes a way to compress an orbifold annotation to sets of such minimal automorphisms. This way a hierarchical annotation is described together with an interpretation of the annotation. Based on this annotation an example is given that illustrates the construction of an automaton for certain pattern matching problems in music processing.
32
Knipe, David Michael. "Automorphisms of the countable generic partial order." Thesis, University of Leeds, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.493772.
Full textAbstract:
The countable generic partial order (P, <) is defined to be the Fraisse limit of the class of finite partially ordered sets. It occurred as part of Schmerl's classification of countable homogeneous partial orders (see [5]). In this thesis I study its automorphisms.
33
Brightwell, Mark. "Lattices and automorphisms of compact complex manifolds." Thesis, University of Glasgow, 1999. http://theses.gla.ac.uk/2803/.
Full textAbstract:
This work makes use of well-known integral lattices to construct complex algebraic varieties reflecting properties of the lattices. In particular the automorphism groups of the lattices are closely related to the symmetries of varieties. The constructions are to two types: generalised Kummer manifolds and toric varieties. In both cases the examples are of the most interest. A generalised Kummer manifold is the resolution of the quotient of a complex torus by some finite group G. A description of the construction for certain cyclic groups G by given in terms of holomorphic surgery of disc bundles. The action of the automorphism groups is given explicitly. The most important example is a compact complex 12-dimensinoal manifold associated to the Leech lattice admitting an action of the finite simple Suzuki group. All these generalised Kummer manifolds are shown to be simply connected. Toric varieties are associated to certain decompositions of Rn into convex cones. The automorphism groups of those associated to Weyl group decompositions of Rn are calculated. These are used to construct 24-dimensional singular varieties from some Neimeier lattices. Their symmetries are extensions of Mathieu groups and their singularities closely related to the Golay codes.
34
Watson, Paul Daniel. "Symmetries and automorphisms of compact Riemann surfaces." Thesis, University of Southampton, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.294489.
Full text
35
Gagnon-Bischoff, Jérémie. "Approximately Inner Automorphisms of von Neumann Factors." Thesis, Université d'Ottawa / University of Ottawa, 2021. http://hdl.handle.net/10393/41879.
Full textAbstract:
Through von Neumann's reduction theory, the classification of injective von Neumann algebras acting on separable Hilbert spaces translates into the classification of injective factors. In his proof of the uniqueness of the injective type II₁ factor, Connes showed an alternate characterization of the approximately inner automorphisms of type II₁ factors. Moreover, he conjectured that this characterization could be extended to all types of factors acting on separable Hilbert spaces. In this thesis, we present a general toolbox containing the basic notions needed to study von Neumann algebras, before describing our work concerning Connes' conjecture in the case of type IIIλ factors. We have obtained partial results towards the proof of a modified version of this conjecture.
36
Schlemmer, Tobias. "Annotating Lattice Orbifolds with Minimal Acting Automorphisms." Technische Universität Dresden, 2012. https://tud.qucosa.de/id/qucosa%3A26138.
Full textAbstract:
Context and lattice orbifolds have been discussed by M. Zickwolff, B. Ganter and D. Borchmann. Preordering the folding automorphisms by set inclusion of their orbits gives rise to further development. The minimal elements of this preorder have a prime group order and any group element can be dissolved into the product of group elements whose group order is a prime power. This contribution describes a way to compress an orbifold annotation to sets of such minimal automorphisms. This way a hierarchical annotation is described together with an interpretation of the annotation. Based on this annotation an example is given that illustrates the construction of an automaton for certain pattern matching problems in music processing.
37
Coleman, Thomas. "Automorphisms and endomorphisms of first-order structures." Thesis, University of East Anglia, 2017. https://ueaeprints.uea.ac.uk/64074/.
Full textAbstract:
In this thesis, we consider questions relating to automorphisms and endomorphisms of countable, relational first-order structures M, with a particular emphasis on bimorphism monoids. We determine semigroup-theoretic results for three types of endomorphism monoid onM, along with generation results whenMis the random graph R or the discrete linear order (N;_). In addition, we introduce three types of partial map monoid ofM, and prove some semigroup-theoretic and generation results in these cases. We introduce the idea of a permutation monoid, and characterise the closed submonoids of the infinite symmetric group Sym(N). Following this, we turn our attention the idea of oligomorphic transformation monoids, and expand on the existing results by considering a range of notions of homomorphismhomogeneity as introduced by Lockett and Truss in 2012. Furthermore, we show that for any finite group G, there exists an oligomorphic permutation monoid with group of units isomorphic to G. The main result of the thesis is an analogue of Fra¨ıss´e’s theorem covering twelve of the eighteen notions of homomorphism-homogeneity; this contains both Fra¨ıss´e’s theorem, and a version of this for MM-homogeneous structures by Cameron and Neˇsetˇril in 2006, as corollaries. This is then used to determine the extent to which some well-known countable homogeneous structures are also homomorphism-homogeneous. Finally, we turn our attention to MB-homogeneous graphs and digraphs. We begin by classifying those homogeneous graphs that are also MB-homogeneous. We then determine an example of an MB-homogeneous graph not in this classification, and use the idea behind this construction to demonstrate 2@0 many non-isomorphic examples of MB-homogeneous graphs. We also give 2@0 many non-isomorphic examples of MB-homogeneous digraphs.
38
Chrétien, Pierre. "Groupes d’Inertie et Variétés Jacobiennes." Thesis, Bordeaux 1, 2013. http://www.theses.fr/2013BOR14785/document.
Full textAbstract:
Soient k un corps algébriquement clos de caractéristique p > 0 et C/k une courbe projective, lisse, intègre de genre g > 1 munie d’un p-groupe d’automorphismes G tel que |G| > 2p/(p-1)g. Le couple (C,G) est appelé grosse action. Si (C,G) est une grosse action, alors |G| <=4p/(p-1)^2g^2 (*). Dans cette thèse, nous étudions les répercussions arithmétiques des propriétés géométriques de grosses actions. Nous étudions d’abord l’arithmétique de l’extension de monodromie sauvage maximale de courbes sur un corps local K d’inégale caractéristique p à corps résiduel algébriquement clos, de genre arbitrairement grand ayant pour potentielle bonne réduction une grosse action satisfaisant le cas d’égalité de (*). On étudie en particulier les conducteurs de Swan attachés à ces courbes. Nous donnons ensuite les premiers exemples, à notre connaissance, de grosses actions (C,G) telles que le groupe dérivé D(G) soit non abélien. Ces courbes sont obtenues comme revêtements de S-corps de classes de rayons de P1(Fq) pour S non vide un sous-ensemble fini de P1(Fq). Enfin, on donne une méthode de calcul des S-corps de classes de Hilbert de revêtements abéliens de la droite projective d’exposant p et supersinguliers que l’on illustre pour des courbes de Deligne-LusztigLet k be an algebraically closed field of characteristic p > 0 and C/k be a projective,smooth, integral curve of genus g > 1 endowed with a p-group of automorphisms G such that |G| > 2p/(p-1)g. The pair (C,G) is called big action. If (C,G) is a big action, then |G|<=4p/(p-1)^2g^2 (*). In this thesis, one studies arithmetical repercussions of geometric properties of big actions. One studies the arithmetic of the maximal wild monodromy extension of curves over a local field K of mixed characteristic p with algebraically closed residue field, with arbitrarily high genus having for potential good reduction a big action achieving equality in (*). One studies the associated Swan conductors. Then, one gives the first examples, to our knowledge, of big actions (C,G) with non abelian derived group D(G). These curves are obtained as coverings of S-ray class fields of P1(Fq) where S is a finite non empty subset of P1(Fq). Finally, one describes a method to compute S-Hilbert class fields of supersingular abelian covers of the projective line having exponent p and one illustrates it for some Deligne-Lusztig curves
39
Donoso, Sebastian Andres. "Contributions to ergodic theory and topological dynamics : cube structures and automorphisms." Thesis, Paris Est, 2015. http://www.theses.fr/2015PEST1007/document.
Full textAbstract:
Cette thèse est consacrée à l'étude des différents problèmes liés aux structures des cubes , en théorie ergodique et en dynamique topologique. Elle est composée de six chapitres. La présentation générale nous permet de présenter certains résultats généraux en théorie ergodique et dynamique topologique. Ces résultats, qui sont associés d'une certaine façon aux structures des cubes, sont la motivation principale de cette thèse. Nous commençons par les structures de cube introduites en théorie ergodique par Host et Kra (2005) pour prouver la convergence dans $L^2 $ de moyennes ergodiques multiples. Ensuite, nous présentons la notion correspondante en dynamique topologique. Cette théorie, développée par Host, Kra et Maass (2010), offre des outils pour comprendre la structure topologique des systèmes dynamiques topologiques. En dernier lieu, nous présentons les principales implications et extensions dérivées de l'étude de ces structures. Ceci nous permet de motiver les nouveaux objets introduits dans la présente thèse, afin d'expliquer l'objet de notre contribution. Dans le Chapitre 1, nous nous attachons au contexte général en théorie ergodique et dynamique topologique, en mettant l'accent sur l'étude de certains facteurs spéciaux. Les Chapitres 2, 3, 4 et 5 nous permettent de développer les contributions de cette thèse. Chaque chapitre est consacré à un thème particulier et aux questions qui s'y rapportent, en théorie ergodique ou en dynamique topologique, et est associé à un article scientifique. Les structures de cube mentionnées plus haut sont toutes définies pour un espace muni d'une unique transformation. Dans le Chapitre 2, nous introduisons une nouvelle structure de cube liée à l'action de deux transformations S et T qui commutent sur un espace métrique compact X. Nous étudions les propriétés topologiques et dynamiques de cette structure et nous l'utilisons pour caractériser les systèmes qui sont des produits ou des facteurs de produits. Nous présentons également plusieurs applications, comme la construction des facteurs spéciaux. Le Chapitre 3 utilise la nouvelle structure de cube définie dans le Chapitre 2 dans une question de théorie ergodique mesurée. Nous montrons la convergence ponctuelle d'une moyenne cubique dans un système muni deux transformations qui commutent. Dans le Chapitre 4, nous étudions le semigroupe enveloppant d'une classe très importante des systèmes dynamiques, les nilsystèmes. Nous utilisons les structures des cubes pour montrer des liens entre propriétés algébriques du semigroupe enveloppant et les propriétés topologiques et dynamiques du système. En particulier, nous caractérisons les nilsystèmes d'ordre 2 par une propriété portant sur leur semigroupe enveloppant. Dans le Chapitre 5, nous étudions les groupes d'automorphismes des espaces symboliques unidimensionnels et bidimensionnels. Nous considérons en premier lieu des systèmes symboliques de faible complexité et utilisons des facteurs spéciaux, dont certains liés aux structures de cube, pour étudier le groupe de leurs automorphismes. Notre résultat principal indique que, pour un système minimal de complexité sous-linéaire, le groupe d'automorphismes est engendré par l'action du shift et un ensemble fini. Par ailleurs, en utilisant les facteurs associés aux structures de cube introduites dans le Chapitre 2, nous étudions le groupe d'automorphismes d'un système de pavages représentatif. La bibliographie, commune à l'ensemble de la thèse, se trouve en fin documentThis thesis is devoted to the study of different problems in ergodic theory and topological dynamics related to og cube structures fg. It consists of six chapters. In the General Presentation we review some general results in ergodic theory and topological dynamics associated in some way to cubes structures which motivates this thesis. We start by the cube structures introduced in ergodic theory by Host and Kra (2005) to prove the convergence in $L^2$ of multiple ergodic averages. Then we present its extension to topological dynamics developed by Host, Kra and Maass (2010), which gives tools to understand the topological structure of topological dynamical systems. Finally we present the main implications and extensions derived of studying these structures, we motivate the new objects introduced in the thesis and sketch out our contributions. In Chapter 1 we give a general background in ergodic theory and topological dynamics given emphasis to the treatment of special factors. % We give basic definitions and describe special factors associated to a From Chapter 2 to Chapter 5 we develop the contributions of this thesis. Each one is devoted to a different topic and related questions, both in ergodic theory and topological dynamics. Each one is associated to a scientific article. In Chapter 2 we introduce a novel cube structure to study the actions of two commuting transformations $S$ and $T$ on a compact metric space $X$. In the same chapter we study the topological and dynamical properties of such structure and we use it to characterize products systems and their factors. We also provide some applications, like the construction of special factors. In the same topic, in Chapter 3 we use the new cube structure to prove the pointwise convergence of a cubic average in a system with two commuting transformations. In Chapter 4, we study the enveloping semigroup of a very important class of dynamical systems, the nilsystems. We use cube structures to show connexions between algebraic properties of the enveloping semigroup and the geometry and dynamics of the system. In particular, we characterize nilsystems of order 2 by its enveloping semigroup. In Chapter 5 we study automorphism groups of one-dimensional and two-dimensional symbolic spaces. First, we consider low complexity symbolic systems and use special factors, some related to the introduced cube structures, to study the group of automorphisms. Our main result states that for minimal systems with sublinear complexity such groups are spanned by the shift action and a finite set. Also, using factors associated to the cube structures introduced in Chapter 2 we study the automorphism group of a representative tiling system. The bibliography is defer to the end of this document
40
梁以豪 and Yee-ho Genthew Leung. "Results related to the embedding conjecture." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B3122474X.
Full text
41
Leung, Yee-ho Genthew. "Results related to the embedding conjecture." Hong Kong : University of Hong Kong, 2000. http://sunzi.lib.hku.hk/hkuto/record.jsp?B22713396.
Full text
42
Hall, Toby Dixon Harold. "Periodicity in chaos : the dynamics of surface automorphisms." Thesis, University of Cambridge, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.387125.
Full text
43
Yasemin, Talu E. "p-groups of automorphisms of compact Riemann surfaces." Thesis, University of Aberdeen, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357987.
Full text
44
Cattaneo, Alberto. "Non-symplectic automorphisms of irreducible holomorphic symplectic manifolds." Thesis, Poitiers, 2018. http://www.theses.fr/2018POIT2322/document.
Full textAbstract:
Nous allons étudier les automorphismes des variétés symplectiques holomorphes irréductibles de type K3^[n], c'est-à-dire des variétés équivalentes par déformation au schéma de Hilbert de n points sur une surface K3, pour n > 1.Dans la première partie de la thèse, nous classifions les automorphismes du schéma de Hilbert de n points sur une surface K3 projective générique, dont le réseau de Picard est engendré par un fibré ample. Nous montrons que le groupe des automorphismes est soit trivial soit engendré par une involution non-symplectique et nous déterminons des conditions numériques et géométriques pour l’existence de l’involution.Dans la deuxième partie, nous étudions les automorphismes non-symplectiques d’ordre premier des variétés de type K3^[n]. Nous déterminons les propriétés du réseau invariant de l'automorphisme et de son complément orthogonal dans le deuxième réseau de cohomologie de la variété et nous classifions leurs classes d’isométrie. Dans le cas des involutions, e des automorphismes d’ordre premier impair pour n = 3, 4, nous montrons que toutes les actions en cohomologie dans notre classification sont réalisées par un automorphism non-symplectique sur une variété de type K3^[n]. Nous construisons explicitement l’immense majorité de ces automorphismes et, en particulier, nous présentons la construction d’un nouvel automorphisme d’ordre trois sur une famille de dimension dix de variétés de Lehn-Lehn-Sorger-van Straten de type K3^[4]. Pour n < 6, nous étudions aussi les espaces de modules de dimension maximal des variétés de type K3^[n] munies d’une involution non-symplectiqueWe study automorphisms of irreducible holomorphic symplectic manifolds of type K3^[n], i.e. manifolds which are deformation equivalent to the Hilbert scheme of n points on a K3 surface, for some n > 1. In the first part of the thesis we describe the automorphism group of the Hilbert scheme of n points on a generic projective K3 surface, i.e. a K3 surface whose Picard lattice is generated by a single ample line bundle. We show that, if it is not trivial, the automorphism group is generated by a non-symplectic involution, whose existence depends on some arithmetic conditions involving the number of points n and the polarization of the surface. We also determine necessary and sufficient conditions on the Picard lattice of the Hilbert scheme for the existence of the involution.In the second part of the thesis we study non-symplectic automorphisms of prime order on manifolds of type K3^[n]. We investigate the properties of the invariant lattice and its orthogonal complement inside the second cohomology lattice of the manifold, providing a classification of their isometry classes. We then approach the problem of constructing examples (or at least proving the existence) of manifolds of type K3^[n] with a non-symplectic automorphism inducing on cohomology each specific action in our classification. In the case of involutions, and of automorphisms of odd prime order for n=3,4, we are able to realize all possible cases. In order to do so, we present a new non-symplectic automorphism of order three on a ten-dimensional family of Lehn-Lehn-Sorger-van Straten eightfolds of type K3^[4]. Finally, for n < 6 we describe deformation families of large dimension of manifolds of type K3^[n] equipped with a non-symplectic involution
45
Shi, Yi. "Perturbations of partially hyperbolic automorphisms on Heisenberg nilmanifold." Thesis, Dijon, 2014. http://www.theses.fr/2014DIJOS048/document.
Full textAbstract:
Dans cette thèse, nous démontrons que les automorphismes partiellement hyperboliques dela nilvariété non Abélienne de dimension 3 peuvent tous être approchés dans la topologie C1 pardes difféomorphismes structurellement stables, chacun possédant un attracteur et un répulseurcomme seuls ensembles récurrents par chaîne. Cela implique que ces automorphismes partiellementhyperboliques ne sont pas robustement transitifs. Nos constructions des attracteurset répulseurs requiérent une analyse des structures de contact invariantes, et des sections deBirkhoff invariante à isotopie dans les fibres près pour ces automorphismes. Comme corollaire,nous en déduisons que les holonomies des feuilletages stables et instables des difféomorphismesapproximants sont des homéomorphismes quasi-périodiquement forcés twistés du cercle, qui sonttransitifs mais pas minimaux, qui satisfont à certaines propriétés de régularité dans les fibresIn this thesis, we show that all the partially hyperbolic automorphisms on the Heisenbergnilmanifold can be C1-approximated by structurally stable C∞ diffeomorphisms which exhibitone attractor and one repeller. This implies that all these automorphisms are not robustly transitive.Our constructions of attractors and repellers need the analysis of dynamical invariantcontact structures and fiber isotopic invariant Birkhoff sections for these automorphisms. Asa corollary, the holonomy maps of stable and unstable foliations of the approximating diffeomorphismsare twisted quasiperiodically forced circle homeomorphisms which are transitive butnon-minimal and satisfying certain fiberwise regularity properties
46
Hummel, Timo [Verfasser]. "Automorphisms of rational projective K*-surfaces / Timo Hummel." Tübingen : Universitätsbibliothek Tübingen, 2021. http://d-nb.info/1228858241/34.
Full text
47
Basson, Dirk (Dirk Johannes). "Parametrizing finite order automorphisms of power series rings." Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/5243.
Full textAbstract:
Thesis (MSc (Mathematics))--University of Stellenboswch, 2010.ENGLISH ABSTRACT: In the work of Green and Matignon it was shown that the Oort-Sekiguchi conjecture is equivalent to a local question of lifting automorphisms of power series rings. The Oort-Sekiguchi conjecture asks when an algebraic curve in characteristic p can be lifted to a relative curve in characteristic 0, while keeping the same automorphism group. The local formulation asks when an automorphism of a power series ring over a field k of characteristic p can be lifted to an automorphism of a power series ring over a discrete valuation ring with residue field k of the same order as the original automorphism. This thesis looks at the local formulation and surveys many of the results for this case. At the end it presents a new theorem giving a Hensel's Lemma type sufficient condition under which lifting is possible.
AFRIKAANSE OPSOMMING: Green en Matignon het bewys dat die Oort-Sekiguchi vermoede ekwivalent is aan `n lokale vraag oor of outomorfismes van magsreeksringe gelig kan word. Die Oort-Sekiguchi vermoede vra of `n algebra ese kromme in karakteristiek p gelig kan word na `n relatiewe kromme in karakteristiek 0, terwyl dit dieselfde outomorfisme groep behou. Die lokale vraag vra wanneer `n outomorfisme van `n magsreeksring oor `n liggaam k van karakteristiek p gelig kan word na `n outomorfisme van `n magsreeksring oor `n diskrete waarderingsring met residuliggaam k, terwyl dit dieselfde orde behou as die aanvanklike outomorfisme. Hierdie tesis fokus op die lokale vraag en bied `n opsomming van baie bekende resultate vir hierdie geval. Aan die einde word `n nuwe stelling aangebied wat voorwaardes stel waaronder hierdie vraag positief beantwoord kan word.
48
Derakhshan, Parisa. "Automorphisms generating disjoint Hamilton cycles in star graphs." Thesis, Loughborough University, 2015. https://dspace.lboro.ac.uk/2134/16779.
Full textAbstract:
In the first part of the thesis we define an automorphism φn for each star graph Stn of degree n-1, which yields permutations of labels for the edges of Stn taken from the set of integers {1,..., [n/2c]}. By decomposing these permutations into permutation cycles, we are able to identify edge-disjoint Hamilton cycles that are automorphic images of a known two-labelled Hamilton cycle H1 2(n) in Stn. The search for edge-disjoint Hamilton cycles in star graphs is important for the design of interconnection network topologies in computer science. All our results improve on the known bounds for numbers of any kind of edge-disjoint Hamilton cycles in star graphs.
49
Costantini, Mauro. "On the lattice automorphisms of certain algebraic groups." Thesis, University of Warwick, 1989. http://wrap.warwick.ac.uk/101705/.
Full textAbstract:
In the first chapter we give an introduction, and a survey of known results, which we shall use throughout the dissertation. In the second chapter we first prove that every projectivity of a connected reductive non-abelian algebraic group G over K = Fp is strictly index-preserving (Theorem 2.1.6.). Then we prove that every autoprojectivity of G induces an automorphism of the building canonically associated to O. Furthermore we show how certain autoprojectivities of G act on the Weyl group of G and on the Dynkin diagram of G. In the third chapter we restrict our attention to simple algebraic groups over K. We prove that if G is a simple algebraic group over K of rank at least 2, then the problem whether every autoprojectivity of G is induced by an automorphism, is reduced to the problem whether every autoprojectivity of G fixing every parabolic subgroup of G is the identity. Namely, if we let Γ(G) – {φε Aut L(G) I Pφ = P for every parabolic subgroup P of G} , we have Aut L(G) = Γ (Aut G)*, where (Aut G)* is the group of all autoprojectivities of G induced by an automorphism (Theorem 3.4.9. and Corollary 3.4.15.). In Chapter 4 we prove that actually Γ = {1} if G has rank at least 3 and p ≠ 2 (Theorem 4.6.5.), while in Chapter 5 we prove the same result , with different arguments, for the case of rank 1 (Corollary 5.2.6.) and 2, type A2 excluded (Corollary 5.3.8.) (for groups of rank 1 we impose no restrictions on p). Finally, in Chapter 6 we show that for the groups of type A2 Theorem 4.6.5. does not hold. For this purpose we construct a non-trivial subgroup of the group Γ(SL3(F23)) (Corollary 6.4.15.).
50
Saleh, Bashar. "Formality and homotopy automorphisms in rational homotopy theory." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-160835.
Full textAbstract:
This licentiate thesis consists of two papers treating subjects in rational homotopy theory. In Paper I, we establish two formality conditions in characteristic zero. We prove that adg Lie algebra is formal if and only if its universal enveloping algebra is formal. Wealso prove that a commutative dg algebra is formal as a dg associative algebra if andonly if it is formal as a commutative dg algebra. We present some consequences ofthese theorems in rational homotopy theory. In Paper II, we construct a differential graded Lie model for the universal cover of the classifying space of the grouplike monoid of homotopy automorphisms of a space that fix a subspace.At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 2: Manuscript.