Thèses sur le sujet « Locally nilpotent »
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1
Wang, Zhiqing. « Locally nilpotent derivations of polynomial rings ». Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0018/NQ48119.pdf.
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Milian, Dagmara. « Locally nilpotent 5-Engel p-groups ». Thesis, University of Oxford, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.561122.
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In this thesis we investigate the structure of locally nilpotent 5-Engel p-groups. We show that for p > 7, locally nilpotent 5-Engel p-groups have class at most 10. This is a global theorem, where the result is not dependent on the number of generators of the group. The proof uses new and established Lie methods and a custom C++ implementation of an algorithm that constructs minimal generating sets and structure constants of multi- graded Lie algebras in a variety defined by three multilinear relations, which hold in the Lie rings associated with 5-Engel p-groups. We obtain our results by calculating in the set Q(p) = {~ I x E Z, yE Z+, Y # 0 modulo any p f/. p} (where p is a set of excluded primes and x, y are arbitrarily large integers), as well as the fields Zp, p prime. We introduce several reduction theorems, making the result possible. We also present results about the normal closure of elements in these groups. We use a Higman reduction theorem and the same custom C++ program to show that locally nilpotent 5-Engel p-groups, p 2: 5, are Fitting, with Fitting degree at most 4 if p > 7, at most 5 if p = 7 and at most 6 if p = 5. These results are best possible.
3
Chitayat, Michael. « Locally Nilpotent Derivations and Their Quasi-Extensions ». Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/35072.
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In this thesis, we introduce the theory of locally nilpotent derivations and use it to compute certain ring invariants.
We prove some results about quasi-extensions of derivations and use them to show that certain rings are non-rigid.
Our main result states that if k is a field of characteristic zero, C is an affine k-domain and
B = C[T,Y] / < T^nY - f(T) >, where n >= 2 and f(T) \in C[T] is such that
delta^2(f(0)) != 0 for all nonzero locally nilpotent derivations delta of C,
then ML(B) != k.
This shows in particular that the ring B is not a polynomial ring over k.
4
Khoury, Joseph. « Locally nilpotent derivations and their rings of constants ». Thesis, University of Ottawa (Canada), 2001. http://hdl.handle.net/10393/9028.
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Given a UFD R containing Q , we study R-elementary derivations of B = R[Y1,..., Ym], i.e., R-derivations satisfying D( Yi) ∈ R for all i; in the particular case of m = 3, we will show that if R is a polynomial ring in n variables over a field k (of characteristic zero), and a1, a3, a3 ∈ R are three monomials, then the kernel of the derivation i=13ai6 /6Yi of B is generated over R by at most three linear elements in the Yi's. This gives a partial answer to a question of A. van den Essen ([27]) about the existence of elementary derivations in dimension six whose kernels are not finitely generated. A set of generators is given for the kernel of R-elementary fixed point free derivations of B. Also, some interesting examples of elementary derivations in dimensions six and seven are provided as well as a criterion for a derivation of R[2] (i.e., a polynomial ring in two variables over R) to be R-elementary. Given a field k of characteristic zero, it is well-known that the kernel of any linear derivation of k[X 1,..., Xn] (that is, a k-derivation which maps each Xi to a linear form in X1,..., Xn) is a finitely generated k-algebra (see [28]). All known proofs of this result are non-constructive in the sense that we do not know a generating set for the kernel. Nowicki conjectured in [25] that the kernel of the derivation d = i=1nXi6 /6Yi of k[X1,..., Xn, Y1,..., Yn] is generated over k by the elements uij = XiYj - XjYi for 1 ≤ i ≤ j ≤ n. Using the theory of Groebner bases, we prove this conjecture in the more general case of the derivation D = i=1nXti i6/6Yi where each ti is a nonnegative integer. Note that in the case of the derivation D, the finite generation of the kernel is no longer evident. Note also that the generators of ker D are linear in the Yi's over k[X1,..., Xn]; we will show that this is not always the case for elementary derivations by giving an example of an elementary derivation in dimension seven whose kernel is finitely generated but cannot be generated by linear forms.
5
EL, Houari Hassan. « Algorithms for locally nilpotent derivations in dimension two and three ». Limoges, 2007. https://aurore.unilim.fr/theses/nxfile/default/7d0e7c9d-8bec-4ccf-af81-92abce4349cb/blobholder:0/2007LIMO4049.pdf.
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Les dérivations localement nilpotentes sur les anneaux des polynômes sont des objets de grande importance dans beaucoup de domaines de mathématiques. Durant la dernière décennie, elles ont connu un véritable progrès et sont devenues un élément essentiel pour la compréhension de la géométrie algébrique affine et d’algèbre commutative. Cette importance est due au fait que certains problèmes classiques dans ces domaines, telles que la conjecture jacobienne, le problème d’élimination, le problème de plongement et le problème de linéarisation, ont été reformulés dans la théorie des dérivations localement nilpotentes. Cette thèse porte sur l’étude algorithmique des problèmes liés aux dérivations localement nilpotentes et leurs applications aux auto-morphismes polynomiaux de l’espace affine. Elle a pour objectif de présenter, d’une part, quelques problèmes dans lesquels les dérivations localement nilpotentes jouent un rôle crucial, à savoir le problème des coordonnées et le problème de paramétrisation polynomial des courbes algébriques dans l’espace affine. Et d’autre part, de donner quelques algorithmes qui peuvent contribuer à la compréhension des dérivations localement nilpotente en dimension trois, à savoir les algorithmes du rang et de triangulabilité des dérivations localement nilpotentesDerivations, especially locally nilpotent ones, over polynomial rings are objects of great importance in many fields of pure and applied mathematics. Nowadays, locally nilpotent derivations have made remarkable progress and became an important topic in understanding affine algebraic geometry and commutative algebra. This is due to the fact that some classic problems in these areas, such as the Jacobian conjecture, the Linearization problem and the Cancellation problem, can be reformulated in terms of locally nilpotent derivations. This thesis is about the algorithmic study of problems linked to locally nilpotent derivations and their applications to the study of polynomial automorphisms of the affine space. Its aim is to present, on one hand, some problems in which locally nilpotent derivations play a crucial role, namely, the coordinate problem and the parametrization problem. On the other hand, give some algorithms concerning locally nilpotent derivations, which may contribute in understanding locally nilpotent derivations in three dimensional case, namely, rang and triangulability algorithms of locally nilpotent derivations
6
Nur, Alexandra. « Locally Nilpotent Derivations and the Cancellation Problem in Affine Algebraic Geometry ». Thesis, University of Ottawa (Canada), 2011. http://hdl.handle.net/10393/28926.
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Let K be a field of characteristic zero and let R [n] denote the polynomial ring in n variables over a ring R for any n ∈ N , n > 0.
We present some basic theory for the study of locally nilpotent derivations as an effective tool in algebraic geometry. Using this tool, we examine the Cancellation Problem in affine algebraic geometry, which asks: Let A be a K -algebra such that A[1] = K [n+1]. Does it follow that A = K [n]? This problem is open for n > 2. We present the solutions to the cases n = 1 and n = 2, in the latter case essentially following the algebraic method of Crachiola and Makar-Limanov [9].
We examine a potential counterexample, R = K [X, Y, Z, T]/⟨X + X ²Y + Z² + T³⟩, referred to as Russell's Cubic. We show that while R closely resembles a polynomial ring in 3 variables, we have that R ≠ K&sqbl0;3&sqbr0; , a result due to Makar-Limanov [25]. This is achieved by showing that the Derksen invariant of R is not equal to the Derksen invariant of K&sqbl0;3&sqbr0; . It is unknown if R[1] is a polynomial ring in 4 variables over K , nonetheless, we examine some properties of R [1] which highlight its similarities with K&sqbl0;4&sqbr0; .
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Nyobe, Likeng Samuel Aristide. « Locally Nilpotent Derivations on Polynomial Rings in Two Variables over a Field of Characteristic Zero ». Thesis, Université d'Ottawa / University of Ottawa, 2017. http://hdl.handle.net/10393/35906.
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The main goal of this thesis is to present the theory of Locally Nilpotent Derivations
and to show how it can be used to investigate the structure of the polynomial ring
in two variables k[X;Y] over a field k of characteristic zero. The thesis gives a com-
plete proof of Rentschler's Theorem, which describes all locally nilpotent derivations
of k[X;Y]. Then we present Rentschler's proof of Jung's Theorem, which partially
describes the group of automorphisms of k[X;Y]. Finally, we present the proof of the
Structure Theorem for the group of automorphisms of k[X;Y].
8
Merighe, Liliam Carsava. « Uma introdução às derivações localmente nilpotentes com uma aplicação ao 14º problema de Hilbert ». Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-05082015-102547/.
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O principal objetivo desta dissertação é estudar um contraexemplo para o Décimo Quarto Problema de Hilbert no caso de dimensão n = 5, que foi apresentado por Arno van den Essen ([6]) em 2006 e que é baseado em um contraexemplo de D. Daigle e G. Freudenburg ([4]). Para isso, serão estudados os conceitos fundamentais da teoria de derivações e os princípios básicos das derivações localmente nilpotentes, bem como seus respectivos corolários. Dentre esses princípios encontra-se o Princípio 13, que garante que, se B é uma k- álgebra polinomial, digamos B = k[x1; ..., xn], (onde k é um corpo de característica zero) e D é uma derivação localmente nilpotente sobre B, então seu núcleo A = ker D satisfaz A = B &cap: Frac(A). Assim encontramos o contraexemplo esperado, ao mostrar que A não é finitamente gerado sobre k. Além disso, no apêndice deste trabalho, é dada uma prova para o caso de dimensão 1 do Décimo Quarto Problema de Hilbert.The main objective of this thesis is to study a counterexample to the Hilberts Fourteenth Problem in dimension n = 5, which was presented by Arno van den Essen ([6]) in 2006 and that is based on a counterexample of D. Daigle and G. Freudenburg ([4]). For these purpose, we study the fundamental concepts of the theory of derivations and the basic principles of locally nilpotent derivations and their corollaries. Among these principles, Principle 13 ensures that if B is a k-algebra polynomial, say B = k[x1; ..., xn], (where k is a field of characteristic zero) and D is a locally nilpotent derivation on B, then its kernel A = ker D satisfies A = B ∩ Frac(A). Once we have proved that A is not finitely generated over k, we find the expected counterexample. In addition, in the appendix of this work is given a proof for the Hilberts Fourteenth Problemin dimension n = 1.
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Abreu, Kelyane Barboza de. « Derivações localmente nilpotentes e os teoremas de Rentschler e Jung ». Universidade Federal da Paraíba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/7438.
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Previous issue date: 2014-02-19Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The main goal of this work is to furnish a proof of the well-known Rentschler s Theorem, which describes the structure of the locally nilpotent derivations on the polynomial ring in two indeterminates (over a field of characteristic zero), up to conjugation by tame automorphisms. As a central application of this result, we prove Jung s Theorem, concerning the generators of the group of automorphisms in two variables. Finally, some examples are discussed, illustrating connections to other important topics.
O principal objetivo deste trabalho é fornecer uma demonstração do bem-conhecido Teorema de Rentschler, que descreve a estrutura das derivações localmente nilpotentes sobre o anel de polinômios em duas variáveis (sobre um corpo de característica zero), a menos de conjugação por automorfismos tame . Como aplicação central deste resultado, provamos o Teorema de Jung, sobre os geradores do grupo de automorfismos em duas variáveis. Finalmente, alguns exemplos são discutidos, ilustrando conexões com outros tópicos importantes.
10
丸橋, 広和. « 単連結べき零Lie群のパラメータ剛性をもつ作用 ». 京都大学 (Kyoto University), 2014. http://hdl.handle.net/2433/188455.
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Hedén, Isac. « Ga-actions on Complex Affine Threefolds ». Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-203708.
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This thesis consists of two papers and a summary. The papers both deal with affine algebraic complex varieties, and in particular such varieties in dimension three that have a non-trivial action of one of the one-dimensional algebraic groups Ga := (C, +) and Gm := (C*, ·). The methods used involve blowing up of subvarieties, the correspondances between Ga - and Gm - actions on an affine variety X with locally nilpotent derivations and Z-gradings respectively on O(X) and passing from a filtered algebra A to its associated graded algebra gr(A). In Paper I, we study Russell’s hypersurface X , i.e. the affine variety in the affine space A4 given by the equation x + x2y + z3 + t2 = 0. We reprove by geometric means Makar-Limanov’s result which states that X is not isomorphic to A3 – a result which was crucial to Koras-Russell’s proof of the linearization conjecture for Gm -actions on A3. Our method consist in realizing X as an open part of a blowup M −→ A3 and to show that each Ga -action on X descends to A3 . This follows from considerations of the graded algebra associated to O(X ) with respect to a certain filtration. In Paper II, we study Ga-threefolds X which have as their algebraic quotient the affine plane A2 = Sp(C[x, y]) and are a principal bundle above the punctured plane A2 := A2 \ {0}. Equivalently, we study affine Ga -varieties Pˆ that extend a principal bundle P over A2, being P together with an extra fiber over the origin in A2. First the trivial bundle is studied, and some examples of extensions are given (including smooth ones which are not isomorphic to A2 × A). The most basic among the non-trivial principal bundles over A2 is SL2 (C) −→ A2, A 1→ Ae1 where e1 denotes the first unit vector, and we show that any non-trivial bundle can be realized as a pullback of this bundle with respect to a morphism A2 −→ A2. Therefore the attention is then restricted to extensions of SL2(C) and find two families of such extensions via a study of the graded algebras associated with the coordinate rings O(Pˆ) '→ O(P ) with respect to a filtration which is defined in terms of the Ga -actions on P and Pˆ respectively.
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Derakhshan, Jamshid. « Problems on nilpotency and local finiteness in infinite groups and infinite dimensional algebras ». Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.362007.
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Neves, Marcus Vinícius de Andrade. « Grupos localmente nilpotentes e o hipercentro local de um grupo ». reponame:Repositório Institucional da UnB, 2008. http://repositorio.unb.br/handle/10482/6589.
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Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2008.Submitted by Jaqueline Ferreira de Souza (jaquefs.braz@gmail.com) on 2009-09-28T19:33:43Z No. of bitstreams: 1 2008_MarcusViniciusAndradeNeves.pdf: 305283 bytes, checksum: 23685840896be87d3dd352190defc44b (MD5)
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A finalidade da presente dissertação é a apresentação de um trabalho recente [1] intitulado On the local hypercenter of a group, de autoria de José Ivan Silva Ramos e Rudolf Maier. Nele o hipercentro local K(G) de um grupo G é introduzido e suas propriedades básicas são estudadas. Particularmente obtém-se extensões de teoremas clássicos de Baer, Mal'cev e McLain sobre grupos localmente nilpotentes. Além disso, abordamos também ligações entre K(G), os subgrupos abnormais e os subgrupos maximais localmente nilpotentes de G. ____________________________________________________________________________ ABSTRACT
The purpose of this dissertation is the presentation of a recent article [1] entitled On the local hypercenter of a group, by Jose Ivan Silva Ramos and Rudolf Maier. In that work the local hypercenter K(G) of a group G is introduced and its basic properties are studied. Particularly extensions of classical theorems of Baer, Mal'cev and McLain on locally nilpotent groups are obtained. We also discuss the links between K(G), abnormal subgroups and the maximal locally nilpotent subgroups of G.
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Monday, Casey R. « A Characterization of Serre Classes of Reflexive Modules Over a Complete Local Noetherian Ring ». UKnowledge, 2014. http://uknowledge.uky.edu/math_etds/13.
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Serre classes of modules over a ring R are important because they describe relationships between certain classes of modules and sets of ideals of R. We characterize the Serre classes of three different types of modules. First we characterize all Serre classes of noetherian modules over a commutative noetherian ring. By relating noetherian modules to artinian modules via Matlis duality, we characterize the Serre classes of artinian modules. A module M is reflexive with respect to E if the natural evaluation map from M to its bidual is an isomorphism. When R is complete local and noetherian, take E as the injective envelope of the residue field of R. The main result provides a characterization of the Serre classes of reflexive modules over a complete local noetherian ring. This characterization depends on an ability to “construct” reflexive modules from noetherian modules and artinian modules. We find that Serre classes of reflexive modules over a complete local noetherian ring are in one-to-one correspondence with pairs of collections of prime ideals which are closed under specialization.
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Frolík, Stanislav. « Geometrická teorie řízení na nilpotentních Lieových grupách ». Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2019. http://www.nusl.cz/ntk/nusl-399583.
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This thesis deals with the theory of geometric control of the trident robot. The thesis describes the basic concepts of differential geometry and control theory, which are subsequently used for describing various mechanisms. Finally, the thesis proposes the management using inferred results.
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Hassani, Ali. « ÉQUATION DES ONDES SUR LES ESPACES SYMÉTRIQUES RIEMANNIENS DE TYPE NON COMPACT ». Phd thesis, Université de Nanterre - Paris X, 2011. http://tel.archives-ouvertes.fr/tel-00669082.
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Ce mémoire porte sur l'étude des équations d'évolution sur des variétés à coubure non nulle, plus particulièrement l'équation des ondes sur les espaces symétriques riemanniens de type non compact. Des propriétés de dispersion des solutions du problème de Cauchy homogène sont démontrées. Ces propriétés sont ensuite utilisées pour établir des estimations dites estimations de Strichartz. L'examen de ces estimées permet de déduire que le problème de Cauchy non linéaire avec des non-linéarités de type puissance est globalement bien posé pour des données initiales petites et localement bien posé pour des données arbitraires. Après un chapitre introductif dédié aux définitions, propriétés algébriques et géométriques des espaces symétriques et à quelques aspects élémentaires d'analyse harmonique sphérique sur ces espaces, un article est présenté : Wave equation on Riemannian symmetric spaces. Cet article contient nos résultats principaux. Dans le dernier chapitre nous présentons en détail deux problèmes ouverts qui prolongent nos travaux. Il s'agit respectivement d'établir le lien entre le comportement asymptotique des estimées et les orbites nilpotentes, et l'étude de l'équation des ondes pour les formes différentielles sur les espaces symétriques.
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Lee, Shao-Chi, et 李詔琦. « On nilpotent elements and locally nilpotent ideals ». Thesis, 2016. http://ndltd.ncl.edu.tw/handle/28329151521401689939.
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碩士國立臺灣大學
數學研究所
104
Motivated by 2-primal rings, NI rings and their associated topological structures, we consider a new class of rings, NL rings, in which the nilpotent elements form a locally nilpotent ideal. We first introduce some basic properties of NL rings, and then study the relationships between NL rings and locally strong prime ideals. Lastly, we give the topological structures induced by NL rings.
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Ju, Ling whe, et 朱玲慧. « Locally Nilpotent Radicals of Nonassociative Algebras ». Thesis, 1994. http://ndltd.ncl.edu.tw/handle/41839144695721425453.
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Francalanci, Giulio. « Nilpotence relations in products of groups ». Doctoral thesis, 2020. http://hdl.handle.net/2158/1197496.
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Let C be a class of groups, let G be a group and A, B two subgroups of G. We will say that A and B are C-connected if for all element a and b belonging respectively to A and B, the group < a, b > is in the class C. In particular we will focus on N-connection, where N is the class of nilpotent groups. Moreover, G is said to be the product of A and B, i.e. G=AB, if and only if for all element g in G, there exists a in A and b in B such that g=ab.
In this thesis, given G=AB where A and B are N-connected subgroups, we discuss how some properties of the subgroups A and B can influence the structure of the whole group G.
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Origlia, Marcos Miguel. « Estructuras localmente conformes Kähler y localmente conformes simplécticas en solvariedades compacta ». Doctoral thesis, 2017. http://hdl.handle.net/11086/5837.
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Tesis (Doctor en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2017.En esta tesis estudiamos las estructuras localmente conformes Kähler (LCK) y localmente conformes simplécticas (LCS) invariantes a izquierda en grupos de Lie, o equivalentemente tales estructuras en álgebras de Lie. Luego se buscan retículos (subgrupos discretos co-compactos) en dichos grupos. De esta manera obtenemos estructuras LCK o LCS en las solvariedades compactas (cociente de un grupo de Lie por un retículo). Específicamente estudiamos las estructuras LCK en solvariedades con estructuras complejas abelianas. Luego describimos explícitamente la estructura de las álgebras de Lie que admiten estructuras de Vaisman. También determinamos los grupos de Lie casi abelianos que admiten estructuras LCK o LCS y además analizamos la existencia de retículos en ellos. Finalmente desarrollamos un método para construir de manera sistemática ejemplos de álgebras de Lie equipadas con estructuras LCK o LCS a partir de un álgebra de Lie que ya admite tales estructuras y una representación compatible.
In this thesis we study left invariant locally conformal Kähler (LCK) structures and locally conformal symplectic structures (LCS) on Lie groups, or equivalently such structures on Lie algebras. Then we analize the existence of lattices (co-compact discrete subgroups) on these Lie groups. Therefore, we obtain LCK or LCS structures on compact solvmanifolds (quotients of a Lie group by a lattice). Specifically we study LCK structures on solvmanifold where the complex structure is abelian. Then we describe the structure of a Lie algebra admitting a Vaisman structure. On the other hand we determine the almost abelian Lie groups equipped with a LCK or LCS structures, and we also analize the existence of lattices on these groups. Finally we construct a method to produce examples of Lie algebras admitting LCK or LCS structures beginning with a Lie algebra with these structures and a compatible representation.