To see the other types of publications on this topic, follow the link: Lie.
Dissertations / Theses on the topic 'Lie'
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 'Lie.'
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
Eddy, Scott M. "Lie Groups and Lie Algebras." Youngstown State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1320152161.
Full text
2
Ahluwalia, Kanwardeep Singh. "Lie bialgebras and Poisson lie groups." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.388758.
Full text
3
Yang, Qunfeng. "Some graded Lie algebra structures associated with Lie algebras and Lie algebroids." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0007/NQ41350.pdf.
Full text
4
Palmieri, Riccardo. "Real forms of Lie algebras and Lie superalgebras." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/9448/.
Full textAbstract:
In questa tesi abbiamo studiato le forme reali di algebre e superalgebre di Lie. Il lavoro si suddivide in tre capitoli diversi, il primo è di introduzione alle algebre di Lie e serve per dare le prime basi di questa teoria e le notazioni. Nel secondo capitolo abbiamo introdotto le algebre compatte e le forme reali. Abbiamo visto come sono correlate tra di loro tramite strumenti potenti come l'involuzione di Cartan e relativa decomposizione ed i diagrammi di Vogan e abbiamo introdotto un algoritmo chiamato "push the button" utile per verificare se due diagrammi di Vogan sono equivalenti. Il terzo capitolo segue la struttura dei primi due, inizialmente abbiamo introdotto le superalgebre di Lie con relativi sistemi di radici e abbiamo proseguito studiando le relative forme reali, diagrammi di Vogan e abbiamo introdotto anche qua l'algoritmo "push the button".
5
Burroughs, Nigel John. "The quantisation of Lie groups and Lie algebras." Thesis, University of Cambridge, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358486.
Full text
6
Krook, Jonathan. "Overview of Lie Groups and Their Lie Algebras." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-275722.
Full textAbstract:
Intuitively, Lie groups are groups that are also smooth. The aim of this thesis is to describe how Lie groups are defined as smooth manifolds, and to look into their properties. To each Lie group there exists an associated vector space, which is called the Lie algebra of the Lie group. We will investigate what properties of a Lie group can be derived from its Lie algebra. As an application, we will characterise all unitary irreducible finite dimensional representations of the Lie group SO(3).Liegrupper kan ses som grupper som även är glatta. Målet med den här rapporten är att definiera Liegrupper som glatta mångfalder, och att undersöka några av liegruppernas egenskaper. Till varje Liegrupp kan man relatera ett vektorrum, som kallas Liegruppens Liealgebra. Vi kommer undersöka vilka egenskaper hos en Liegrupp som kan härledas från dess Liealgebra. Som tillämpning kommer vi karaktärisera alla unitära irreducibla ändligtdimensionella representationer av Liegruppen SO(3).
7
Aminou, Adérodjou A. Rachidi. "Groupes de Lie-Poisson et bigèbres de Lie." Lille 1, 1988. http://www.theses.fr/1988LIL10139.
Full textAbstract:
Un groupe de lie-poisson est un groupe de lie g muni d'une structure de poisson telle que la multiplication soit un morphisme de poisson de g x g dans g. L'algebre de lie d'un groupe de lie-poisson porte une structure supplementaire qui en fait une bigebre de lie. Nous etudions les bigebres de lie (autodualite, triplets de manin) et les algebres de lie bicroisees qui generalisent des bigebres de lie. Nous considerons le cas des bigebres de lie exactes, en particulier des bigebres de lie quasitriangulaires et nous etudions plusieurs exemples. Nous montrons que la categorie des bigebres de lie quasi-triangulaires est isomorphe a la categorie des algebres de lie-semenov. Nous comparons la notion de carre d'une algebre de lie-semenov due a semenov-trian-shansky et la notion de double d'une bigebre de lie due a drinfeld. Enfin, nous demontrons le "troisieme theoreme de lie" pour les groupes de lie-poisson et nous etudions les structures de poisson sur un groupe de lie definies par des solutions des equations de yang-baxter classique, generalisee ou modifiee.
8
Aminou, Adérodjou A. Rachidi. "Groupes de Lie-Poisson et bigèbres de Lie." Grenoble 2 : ANRT, 1988. http://catalogue.bnf.fr/ark:/12148/cb37611312n.
Full text
9
Höglund, Joel. "Lie-algebror." Thesis, Uppsala universitet, Algebra och geometri, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-202056.
Full text
10
Mihaylishin, P. A. "Lie detector." Thesis, Сумський державний університет, 2012. http://essuir.sumdu.edu.ua/handle/123456789/28533.
Full text
11
Androulidakis, Iakovos E. "Extensions, cohomology and classification for Lie algebroids and Lie groupoids." Thesis, University of Sheffield, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.369963.
Full text
12
Traustason, Gunnar. "Engel Lie algebras." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334292.
Full text
13
Tullini, Yvonne. "Corrispondenza fra i Gruppi di Lie e le Algebre di Lie." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/16414/.
Full textAbstract:
L'oggetto della tesi è lo studio della corrispondenza tra i gruppi di Lie e le algebre di Lie, mediante in particolare l'applicazione esponenziale. Quindi in primo luogo sarà esaustivamente trattata la teoria delle algebre di Lie e dei gruppi di Lie, così come le proprietà dell'applicazione esponenziale. In seguito saranno introdotti strumenti come i gruppi a un parametro, le coordinate logaritmiche e le azioni destre e sinistre. Infine saranno forniti importanti risultati dati dalla corrispondenza, per esempio che due gruppi di Lie sono localmente isomorfi se e solo se lo sono le relative algebre di Lie e che la corrispondenza si può trovare anche nell'ambito di sottogruppi e sottoalgebre di Lie.
14
Duong, Minh-Thanh. "A new invariant of quadratic lie algebras and quadratic lie superalgebras." Phd thesis, Université de Bourgogne, 2011. http://tel.archives-ouvertes.fr/tel-00673991.
Full textAbstract:
In this thesis, we defind a new invariant of quadratic Lie algebras and quadratic Lie superalgebras and give a complete study and classification of singular quadratic Lie algebras and singular quadratic Lie superalgebras, i.e. those for which the invariant does not vanish. The classification is related to adjoint orbits of Lie algebras o(m) and sp(2n). Also, we give an isomorphic characterization of 2-step nilpotent quadratic Lie algebras and quasi-singular quadratic Lie superalgebras for the purpose of completeness. We study pseudo-Euclidean Jordan algebras obtained as double extensions of a quadratic vector space by a one-dimensional algebra and 2-step nilpotent pseudo-Euclidean Jordan algebras, in the same manner as it was done for singular quadratic Lie algebras and 2-step nilpotent quadratic Lie algebras. Finally, we focus on the case of a symmetric Novikov algebra and study it up to dimension 7.
15
Santacruz, Camilo Andres Angulo. "A cohomology theory for Lie 2-algebras and Lie 2-groups." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-15022019-084657/.
Full textAbstract:
In this thesis, we introduce a new cohomology theory associated to a Lie 2-algebras and a new cohomology theory associated to a Lie 2-group. These cohomology theories are shown to extend the classical cohomology theories of Lie algebras and Lie groups in that their second groups classify extensions. We use this fact together with an adapted van Est map to prove the integrability of Lie 2-algebras anew.Nesta tese, nós introduzimos uma nova teoria de cohomologia associada às 2-álgebras de Lie e uma nova teoria de cohomologia associada aos 2-grupos de Lie. Prova-se que estas teorias de cohomologia estendem as teorias de cohomologia clássicas de álgebras de Lie e grupos de Lie em que os seus segundos grupos classificam extensões. Finalmente, usaremos estos fatos junto com um morfismo de van Est adaptado para encontrar uma nova prova da integrabilidade das 2-álgebras de Lie.
16
Remm, Elisabeth. "Structures affines sur les algébres de Lie et opérades Lie admissibles." Mulhouse, 2001. http://www.theses.fr/2001MULH0670.
Full textAbstract:
Le but de ce travail est l'étude et la construction de structures affines sur une algèbre de Lie, ce qui correspond au problème d'existence de connexions affines, sans courbure ni torsion, invariantes à gauche sur un groupe de Lie. L'existence d'une telle structure munit l'espace vectoriel sous-jacent à l'algèbre de Lie d'une autre structure d'algèbre appelée algèbre symétrique gauche ou algèbre de Vinberg qui, par antisymétrie, redonne la structure d'algèbre de Lie. On étudie également la complétude de la structure et on définit un produit scalaire associé permettant dans certains cas de munir un groupe de Lie associé d'une structure hessienne. On propose ici une approche de ces algèbres au travers des algèbres Lieadmissibles. Par définition, une algèbre est Lie-admissible si le produit X. Y vérifie que X. Y-Y. X est un crochet de Lie. La classe des algèbres Lie-admissibles contient en particulier les algèbres de Lie, de Vinberg et associatives. La variété algébrique des algèbres Lie-admissibles est naturellement fibrée au-dessus de la variété des algèbres de Lie. Le problème d'existence d'une structure affine revient à examiner l'intersection de la sous-variété des algèbres de Vinberg avec les fibres. L'idée de déformer une structure d'algèbre de Lie considérée comme algèbre Lie-admissible en une structure d'algèbre de Vinberg appartenant à la même fibre est donc naturelle. Ceci conduit à définir de manière précise les cohomologies de ces algèbres et à connaître précisemment leurs opérades associées. La deuxième approche est plus géométrique. On montre que les algèbres filiformes non caractéristiquement nilpotentes sont affines. On étudie également toutes les structures affines sur les algèbres abéliennes de dimensions 2 et 3 (en particulier les structures non complètes). On donne les conditions algébriques nécessaires à l'obtention d'une structure sur une algèbre de Lie de contact à partir d'une extension centrale d'une algèbre symplectique.
17
Duong, Minh thanh. "A new invariant of quadratic lie algebras and quadratic lie superalgebras." Thesis, Dijon, 2011. http://www.theses.fr/2011DIJOS021/document.
Full textAbstract:
Dans cette thèse, nous définissons un nouvel invariant des algèbres de Lie quadratiques et des superalgèbres de Lie quadratiques et donnons une étude et classification complète des algèbres de Lie quadratiques singulières et des superalgèbres de Lie quadratiques singulières, i.e. celles pour lesquelles l’invariant n’est pas nul. La classification est en relation avec les orbites adjointes des algèbres de Lie o(m) et sp(2n). Aussi, nous donnons une caractérisation isomorphe des algèbres de Lie quadratiques 2-nilpotentes et des superalgèbres de Lie quadratiques quasi-singulières pour le but d’exhaustivité. Nous étudions les algèbres de Jordan pseudoeuclidiennes qui sont obtenues des extensions doubles d’un espace vectoriel quadratique par une algèbre d’une dimension et les algèbres de Jordan pseudo-euclidienne 2-nilpotentes, de la même manière que cela a été fait pour les algèbres de Lie quadratiques singulières et des algèbres de Lie quadratiques 2-nilpotentes. Enfin, nous nous concentrons sur le cas d’une algèbre de Novikov symétrique et l’étudions à dimension 7In this thesis, we defind a new invariant of quadratic Lie algebras and quadratic Lie superalgebras and give a complete study and classification of singular quadratic Lie algebras and singular quadratic Lie superalgebras, i.e. those for which the invariant does not vanish. The classification is related to adjoint orbits of Lie algebras o(m) and sp(2n). Also, we give an isomorphic characterization of 2-step nilpotent quadratic Lie algebras and quasi-singular quadratic Lie superalgebras for the purpose of completeness. We study pseudo-Euclidean Jordan algebras obtained as double extensions of a quadratic vector space by a one-dimensional algebra and 2-step nilpotent pseudo-Euclidean Jordan algebras, in the same manner as it was done for singular quadratic Lie algebras and 2-step nilpotent quadratic Lie algebras. Finally, we focus on the case of a symmetric Novikov algebra and study it up to dimension 7
18
Ben, Abdeljelil Amine. "Generalized Derivations of Ternary Lie Algebras and n-BiHom-Lie Algebras." Scholar Commons, 2019. https://scholarcommons.usf.edu/etd/7743.
Full textAbstract:
We generalize the results of Leger and Luks and other researchers about generalized derivations to the cases of ternary Lie algebras and n-BiHom Lie algebras. We investigate the derivations algebras of ternary Lie algebras induced from Lie algebras, we explore the subalgebra of quasi-derivations and give their properties. Moreover, we give a classification of the derivations algebras for low dimensional ternary Lie algebras.
For the class of n-BiHom Lie algebras, we study the algebras of generalized derivations and prove that the algebra of quasi-derivations can be embedded in the derivation algebra of a larger n-BiHom Lie algebra.
19
Wickramasekara, Sujeewa, and sujeewa@physics utexas edu. "On the Representations of Lie Groups and Lie Algebras in Rigged Hilbert." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi994.ps.
Full text
20
Ammar, Gregory, Christian Mehl, and Volker Mehrmann. "Schur-Like Forms for Matrix Lie Groups, Lie Algebras and Jordan Algebras." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501032.
Full textAbstract:
We describe canonical forms for elements of a classical Lie group of matrices under similarity transformations in the group. Matrices in the associated Lie algebra and Jordan algebra of matrices inherit related forms under these similarity transformations. In general, one cannot achieve diagonal or Schur form, but the form that can be achieved displays the eigenvalues of the matrix. We also discuss matrices in intersections of these classes and their Schur-like forms. Such multistructered matrices arise in applications from quantum physics and quantum chemistry.
21
Bagnoli, Lucia. "Z-graded Lie superalgebras." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/14118/.
Full textAbstract:
This thesis investigates the role of filtrations and gradings in the study of Lie superalgebras. The main connections between the Z-grading of a Lie superalgebra and its structure are explained. As an example, the simplicity of the Lie superalgebras W(m,n) and S(m,n) is proved. Finally, the strongly symmetric gradings of length three and five of the Lie superalgebras W(m,n) and S(m,n) are classified.
22
Williams, Michael Peretzian. "Nilpotent N-Lie Algebras." NCSU, 2004. http://www.lib.ncsu.edu/theses/available/etd-02162004-083708/.
Full textAbstract:
In 1986, Kasymov introduced the concept of nilpotent $n$-Lie algebras, proved an analogue of Engel's Theorem and later proved an analog of Jacobson's refinement of Engel's Theorem. Despite these achievements, the subject of nilpotency in $n$-Lie algebras has not been examined in great detail in the literature since. We shall explore the concept of nilpotent $n$-Lie algebras by examining, and proving where possible, other classical nilpotent group theory and nilpotent Lie algebra results, in the $n$-Lie algebra setting.
23
Levene, Rupert Howard. "Lie semigroup operator algebras." Thesis, Lancaster University, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.421841.
Full text
24
Street, C. N. H. "Lie detection : cognitive processes." Thesis, University College London (University of London), 2013. http://discovery.ucl.ac.uk/1414942/.
Full textAbstract:
How do we make decisions when we are uncertain? In more real-world settings there is often a vast array of information available to guide the decision, from an understanding of the social situation, to prior beliefs and experience, to information available in the current environment. Yet much of the research into uncertain decision-making has typically studied the process by isolating it from this rich source of information that decision-makers usually have available to them. This thesis takes a different approach. To explore how decisions are made under uncertainty in more real-world settings, this thesis considers how raters decide if someone is lying or telling the truth. Because people are skilled liars, there is little information available to make a definitive decision. How do raters negotiate the ambiguous environment to reach a decision? Raters show a truth bias, which is to say they judge statements as truthful more often than they are so. Recent research has begun to consider dual process theories, suggesting there are two routes for processing information. They claim the truth bias results from an error-prone processing route, but that a more effortful and analytical processing route may overcome it. I will generate a set of testable hypotheses that arise from the dual process position and show that the theory does not stand up to the test. The truth bias can be better explained as resulting from a single process that attempts to make the most 3 informed guess despite being uncertain. To make the informed guess, raters come to rely on context-relevant information when the behaviour of the speaker is not sufficiently diagnostic. An adaptive decision maker position is advocated. I propose the truth bias is an emergent property of making the best guess. That is, in a different context where speakers may be expected to lie, a bias towards disbelieving should be seen. I argue context-dependency is key to understanding decision-making under uncertainty.
25
Lacerda, Conrado Damato de 1986. "Grupos de Lie compactos." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305808.
Full textAbstract:
Orientador: Luiz Antonio Barrera San MartinDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
Made available in DSpace on 2018-08-18T06:52:41Z (GMT). No. of bitstreams: 1 Lacerda_ConradoDamatode_M.pdf: 1208692 bytes, checksum: 167da419a80e3fe06963795a1b3fea2d (MD5) Previous issue date: 2011
Resumo: Neste trabalho apresentamos os principais resultados da teoria dos grupos de Lie compactos e provamos o Teorema de Weyl sobre os seus grupos fundamentais
Abstract: In this work we present the main results about compact Lie groups and prove Weyl's Theorem on their fundamental groups
Mestrado
Teoria de Lie
Mestre em Matemática
26
Almeida, Luis Roberto Lucinger de 1983. "Simetrias de Lie estocásticas." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306332.
Full textAbstract:
Orientador: Pedro José CatuognoTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
Made available in DSpace on 2018-08-20T05:04:07Z (GMT). No. of bitstreams: 1 Almeida_LuisRobertoLucingerde_D.pdf: 4124910 bytes, checksum: 249249a4a4959e28b63a5f2e7290a5fe (MD5) Previous issue date: 2012
Resumo: Nesta tese, estudamos equações diferenciais estocásticas, sob o ponto de vista da teoria das simetrias de Lie. Introduzimos o conceito de simetria de Lie estocástica, que consiste em uma ação que mantém invariante as soluções de uma equação diferencial, onde tal ação é estocástica, isto é, dada por um fluxo estocástico. Nosso principal resultado consiste nas equações de Lie para as simetrias estocásticas, permitindo detectar quando um fluxo estocástico é uma simetria estocástica. Além disso, apresentamos uma possível definição de coordenada canônica para as simetrias estocásticas e obtemos condições, assim como no caso clássico, para encontrá-la. Por fim, mostramos como obter, sistematicamente, transformações entre equações estocásticas
Abstract: In this thesis, we study stochastic differential equations, under the point of view of Lie point symmetries. We introduce the concept of stochastic Lie point symmetry, which consists of an action that keeps invariant the solutions of a differential equation, where such action is stochastic, i.e., given by a stochastic flow. Our main result is the Lie's equations for stochastic symmetries, which allows one to detect when a stochastic flow is a stochastic symmetry. Furthermore, we present a possible definition of canonical coordinates for the stochastic symmetries and we obtain conditions, like in the standard case, to find them. At last, we show how to obtain, systematically, transformations between stochastic differential equations
Doutorado
Matematica
Doutor em Matemática
27
Chloup-Arnould, Véronique. "Groupes de Lie-Poisson." Metz, 1996. http://docnum.univ-lorraine.fr/public/UPV-M/Theses/1996/Chloup_Arnould.Veronique.SMZ9619.pdf.
Full textAbstract:
Dans cette thèse nous étudions les structures de Lie-Poisson. De manière plus précise deux thèmes sont abordés. Le premier est de nature classificatoire. Nous donnons une description complète des algèbres de Manin (c'est-à-dire les grandes algèbres d'un triple de Manin) associées à des structures de bigèbre de lie sur une algèbre de lie réelle semi-simple. Ensuite, en adaptant au cas réel les résultats de Belavin et Drinfeld décrivant les solutions de l'équation de Yang-Baxter standard modifiée non nulle sur une algèbre de lie semi-simple complexe, nous donnons les solutions générales de l'équation de Yang-Baxter modifiée standard non nulle sur une algèbre de lie réelle semi-simple. Enfin nous donnons des résultats partiels concernant les structures de bigèbre liées aux solutions de l'équation de Yang-Baxter modifiée non standard sur une algèbre de lie réelle simple telle que sa complexifiée ne soit pas simple. Le deuxième thème est celui de la linéarisation locale d'une structure de lie-poisson. Nous montrons, en utilisant le théorème de linéarisation analytique dans le cas d'une structure de poisson de j. Conn, que si (g,p) est un groupe de lie-poisson, et si l'algèbre duale est la somme directe d'un idéal semi-simple et d'un idéal abélien, alors p est analytiquement linéarisable dans un voisinage de l'identité. Dans le cadre d'une structure de poisson générale cette proposition peut-être mise en défaut. Nous montrons par ailleurs que toute structure de lie-poisson exacte sur un groupe de lie nilpotent de pas deux est linéaire, sur un groupe de lie nilpotent de pas trois et de dimension inferieure ou égale a six est linéarisable et qu'il existe des structures de lie-poisson exactes sur un groupe de lie nilpotent de pas quatre et de dimension cinq qui ne sont pas linéarisables
28
Öhrnell, Carl. "Lie Groups and PDE." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-420706.
Full text
29
CHLOUP-ARNOULD, VERONIQUE GUTT S. "GROUPES DE LIE-POISSON /." [S.l.] : [s.n.], 1996. ftp://ftp.scd.univ-metz.fr/pub/Theses/1996/Chloup_Arnould.Veronique.SMZ9619.pdf.
Full text
30
Benayadi, Saïd. "Etude d'une famille d'algèbres de Lie généralisant les algèbres de Lie semi-simples." Dijon, 1993. http://www.theses.fr/1993DIJOS001.
Full textAbstract:
Le but de cette thèse est d 'étudier les algèbres de Lie g qui vérifient g,g=g, Ders(g)=ad(g) et z(g)=0, qu'on appelle les algèbres de Lie sympathiques. On construit une algèbre de Lie sympathique non semi-simple qui vérifie h#2(g,g)=0, par conséquent g est rigide par déformation. Ce qui prouve que la structure sympathique n'est pas une dégénérescence directe de la structure semi-simple (par contraction). On construit une algèbre de Lie sympathique de dimension 48 non rigide par déformation. On construit une algèbre de Lie sympathique non semi-simple de dimension 25. Cette algèbre de Lie est la plus petite algèbre de Lie sympathique non semi-simple, connue à ce jour. On montre que certaines propriétés classiques des algèbres de Lie semi-simples restent vraies pour les algèbres de Lie sympathiques. Si g est une algèbre de Lie, on montre que g possède un plus grand idéal sympathique m, et qu'il existe un idéal résoluble de g note p(g) qui est le plus grand idéal l de g tel que lm=0. On montre l'existence d'une sous-algèbre de Lie sympathique m de g telle que g=m+p(g); et g est sympathique si, et seulement si p(g)=0. On étudie: les idéaux l d'une algèbre de Lie g tel que g/l est sympathique; une classe particulière d'algèbres de Lie parfaites; les algèbres de Lie munies d'un produit scalaire invariant
31
Meyer, Philippe. "Représentations associées à des graduations d'algèbres de Lie et d'algèbres de Lie colorées." Thesis, Strasbourg, 2019. http://www.theses.fr/2019STRAD001/document.
Full textAbstract:
Soit k un corps de caractéristique différente de 2 et de 3. Les algèbres de Lie colorées généralisent à la fois les algèbres de Lie et les superalgèbres de Lie. Dans cette thèse on étudie des représentations V d'algèbres de Lie colorées g provenant de structures d'algèbres de Lie colorées sur l'espace vectoriel g⨁V. En premier lieu, on s'intéresse à la structure générale des algèbres de Lie simples de dimension 3 sur k. Puis, on classifie à isomorphisme près les superalgèbres de Lie de dimension finie dont la partie paire est une algèbre de Lie simple de dimension 3. Ensuite, pour un groupe abélien ᴦ et un facteur de commutation ɛ de ᴦ, on développe l'algèbre multilinéaire associée aux espaces vectoriels ᴦ-gradués. Dans ce contexte, les algèbres de Lie colorées jouent le rôle des algèbres de Lie. Ce langage nous permet d'énoncer et prouver un théorème de reconstruction d'une algèbre de Lie colorée ɛ-quadratique g⨁V à partir d'une représentation ɛ-orthogonale V d'une algèbre de Lie colorée ɛ-quadratique g. Ce théorème fait intervenir un invariant qui prend ses valeurs dans la ɛ-algèbre extérieure de V et généralise des résultats de Kostant et Chen-Kang. Puis, on introduit la notion de représentation ɛ-orthogonale spéciale V d'une algèbre de Lie colorée ɛ-quadratique g et on montre qu'elle permet de définir une structure d'algèbre de Lie colorée ɛ-quadratique sur l'espace vectoriel g⨁sl(2,k)⨁V⨂k². Enfin on donne des exemples de représentations ɛ-orthogonales spéciales, notamment des représentations orthogonales spéciales d'algèbres de Lie dont : une famille à un paramètre de représentations de sl(2,k)xsl(2,k) ; la représentation fondamentale de dimension 7 d'une algèbre de Lie de type G₂ ; la représentation spinorielle de dimension 8 d'une algèbre de Lie de type so(7)Let k be a field of characteristic not 2 or 3. Colour Lie algebras generalise both Lie algebras and Lie superalgebras. In this thesis we study representations V of colour Lie algebras g arising from colour Lie algebras structures on the vector space g⨁V. Firstly, we study the general structure of simple three-dimensional Lie algebras over k. Then, we classify up to isomorphism finite-dimensional Lie superalgebras whose even part is a simple three-dimensional Lie algebra. Next, to an abelian group ᴦ and a commutation factor ɛ of ᴦ, we develop the multilinear algebra associated to ᴦ-graded vector spaces. In this context, colour Lie algebras play the rôle of Lie algebras. This language allows us to state and prove a theorem reconstructing an ɛ-quadratic colour Lie algebra g⨁V from an ɛ-orthogonal representation V of an ɛ-quadratic colour Lie algebra g. This theorem involves an invariant taking its values in the ɛ-exterior algebra of V and generalises results of Kostant and Chen-Kang. We then introduce the notion of a special ɛ-orthogonal representation V of an ɛ-quadratic colour Lie algebra g and show that it allows us to define an ɛ-quadratic colour Lie algebra structure on the vector space g⨁sl(2,k)⨁V⨂k². Finally we give examples of special ɛ-orthogonal representations and in particular examples of special orthogonal representations of Lie algebras amongst which are: a one-parameter family of representations of sl(2,k)xsl(2,k) ; the 7-dimensional fundamental representation of a Lie algebra of type G₂ ; the 8-dimensional spinor representation of a Lie algebra of type so(7)
32
Monaro, Merylin. "Lie detection in the future: the online lie detection via human-computer interaction." Doctoral thesis, Università degli studi di Padova, 2018. http://hdl.handle.net/11577/3427259.
Full textAbstract:
Half the people in the Planet Earth are now on internet, surfing the web, keeping connection with the outside world, using online services and interacting in social networks. However, the spread of internet is going hand in hand with the growing malicious use of it. Creating fake social network profiles, wide spreading fake news, posting fake reviews, identity theft to perpetuate online financial frauds are only few examples. To face these problems, all the big internet compa-nies, like Google and Facebook, are now taking the direction towards the online lie detection re-search. The present work is a contribution to online deception detection through the study of com-puter-user interaction. After a brief review of the current lie detection methods, focusing on their advantages and disadvantages for online application, a series of proof of concept experiments are reported. Experiments were conducted measuring indices deriving from three different tools of human-computer interaction: reaction times on keyboard, keystroke dynamics and mouse dynam-ics. Two strategies were used to increase liars’ cognitive load and facilitate the observation of distinctive features of deception: unexpected questions and complex questions. Experiments fo-cused on the deception about identity, as it is a very hot issue and represents a current challenge for companies that provide online services. Participants were asked to respond lying or truth tell-ing to questions that appeared on the computer screen, typing the response, clicking on it with the mouse or pressing one of two alternative keys on keyboard. Data collected from liars and truth-tellers’ responses were analyzed and used to train machine learning classification models. Classi-fication accuracies in distinguishing liars from truth-tellers ranged from 80% to 95%, depending on the deceptive task. Results have proved that it is possible to spot liars analyzing their interac-tion with the computer during the act of lie. In particular, we demonstrated that keystroke dynam-ics is a very promising tool for covert lie detection and it is easily integrable with the online exist-ing applications. Moreover, we confirmed that the cognitive complexity of the deceptive task in-creases the possibility to detect deception.Metà delle persone sul nostro Pianeta navigano nel web, utilizzano servizi online e interagiscono attraverso i social network. Tuttavia, la diffusione di Internet sta andando di pari passo l’uso malevole di esso. La creazione di profili suoi social network, la diffusione di notizie false, il post di recensioni false, le frodi finanziarie online, sono solo alcuni esempi. Per far fronte a queste problematiche, le più grandi compagnie, come Google e Facebook, stanno avviando la ricerca nell’ambito della rilevazione della menzogna online. Il presente lavoro è un contributo alla rilevazione della menzogna online attraverso lo studio dell'interazione tra computer e utente. Dopo una breve rassegna degli attuali metodi di rilevamento della menzogna, concentrandosi sui loro vantaggi e svantaggi per l'applicazione online, vengono riportati una serie di esperimenti. Gli esperimenti sono stati condotti misurando gli indici derivanti da tre diversi strumenti di interazione uomo-macchina: I tempi di reazione su tastiera, la dinamica di battitura su tastiera e la dinamica di movimento del mouse. Sono state utilizzate due strategie per aumentare il carico cognitivo dei soggetti mentitori e facilitare l'osservazione delle caratteristiche peculiari dell'inganno: la tecnica delle domande inaspettate e la tecnica delle domande complesse. Gli esperimenti si sono concentrati sullo studio della menzogna relativa all'identità, dato che si tratta di un tema molto attuale e rappresenta una sfida per le aziende che forniscono servizi online. Ai partecipanti è stato chiesto di rispondere mentendo o dicendo verità alle domande che apparivano sullo schermo del computer, digitando la risposta sulla tastiera, facendo click su di essa con il mouse o premendo uno tra due tasti alternativi di risposta. I dati raccolti dai mentitori e le risposte dei soggetti sinceri sono stati analizzati e utilizzati per costruire modelli di classificazione tramite l’uso di tecniche di apprendimento automatico. L'accuratezza della classificazione nel distinguere i soggetti mentitori dai sinceri varia dall' 80% al 95%, a seconda del paradigma sperimentale utilizzato. I risultati hanno dimostrato che è possibile individuare I soggetti che mentono analizzando la loro interazione con il computer durante l'atto di mentire. In particolare, abbiamo dimostrato che la dinamica di battitura su tastiera rappresenta uno strumento molto promettente per il rilevamento della menzogna, ed è facilmente integrabile con le applicazioni online già esistenti. Inoltre, abbiamo confermato che la complessità cognitiva del compito aumenta la possibilità di individuare la menzogna.
33
Jimenez, William. "Riemannian submersions and Lie groups." College Park, Md. : University of Maryland, 2005. http://hdl.handle.net/1903/2648.
Full textAbstract:
Thesis (Ph. D.) -- University of Maryland, College Park, 2005.Thesis research directed by: Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
34
Alekseevsky, Dmitri, Peter W. Michor, Wolfgang Ruppert, and Peter Michor@esi ac at. "Extensions of Super Lie Algebras." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi980.ps.
Full text
35
Furutsu, Hirotoshi. "Representations of Lie Superalgebras, II." 京都大学 (Kyoto University), 1991. http://hdl.handle.net/2433/168802.
Full textAbstract:
本文データは平成22年度国立国会図書館の学位論文(博士)のデジタル化実施により作成された画像ファイルを基にpdf変換したものであるKyoto University (京都大学)
0048
新制・課程博士
理学博士
甲第4695号
理博第1293号
新制||理||720(附属図書館)
UT51-91-E66
京都大学大学院理学研究科数学専攻
(主査)教授 平井 武, 教授 池部 晃生, 教授 岩崎 敷久
学位規則第5条第1項該当
36
Milson, Robert. "Multi-dimensional Lie-algebraic operators." Thesis, McGill University, 1995. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=40197.
Full textAbstract:
We investigate the geometric properties of multi-dimensional Lie-algebraic operators. Such operators are relevant to the study of quasi-exactly solvable, quantum mechanical systems. The present effort addresses several issues raised by the Q.E.S. research program. One such issue is the normalizability of an operator to Schrodinger form; this criterion is known as the operator closure conditions. We give a geometric, and a representation-theoretic reformulation of the closure conditions, and then use these techniques to obtain solutions for the case of linear SL(2) actions in the plane.The study of multi-dimensional Lie-algebraic operators benefits from an intrinsic, geometrically based approach. We do this by taking as our setting the fibre bundle $ pi$: G $ to$ M, where G is a Lie group, and the base is a homogeneous space. The symbol of a second-order Lie-algebraic operator induces a pseudo-Riemannian metric tensor, g, on the base; the symbol also induces a horizontal-vertical decomposition of the above bundle. Not surprisingly, the geometry of g is determined by this decomposition, and thus allows us to investigate g in terms of the horizontal and vertical vector fields associated to the decomposition.
Of particular interest is the class of flat geometries induced by Lie algebraic operators. One motivation for considering this class is furnished by Turbiner's Conjecture, which states that a Lie algebraic operator admits separation of variables if its symbol induces a flat metric. In the planar case we prove a global result to the effect that a flat, Riemannian manifold of the type described above, is isometric to the quotient of the Euclidean plane by reflections. We then use this result to give a proof of a limited form of Turbiner's conjecture.
37
Alajaji, Sami E. (Sami Emmanuel). "Central filtrations of Lie algebras." Thesis, McGill University, 1995. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=22714.
Full textAbstract:
Consider L to be a graded free Lie algebra over a principal ideal domain, and r a nonzero element of L such that its leading term s, i.e. its homogeneous component of highest order, is not a proper multiple. The main result we show in this thesis is that the graded ideal of leading terms of elements in R = (r) is equal to the ideal generated by the element s. As a consequence we prove that the center of L/R is trivial if the rank of the free Lie algebra L is greater than two.
38
Brodzki, Jacek. "Cyclic cohomology and Lie cochains." Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.257657.
Full text
39
Shrader, Kyle. "Jack Kerouac Does Not Lie." Master's thesis, University of Central Florida, 2006. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/6224.
Full textAbstract:
"Jack Kerouac Does Not Lie" recounts my pilgrimage in the summer of 2000, from southwest Florida to a canyon beach in California where Jack Kerouac—as I had read in his Big Sur—lost his mind forty years earlier. I was heavily influenced. Kerouac's On the Road
showed me what to do with myself. Big Sur showed me where to go. In the twentieth century Americans shifted their notions of the west coast from a means for sustenance to a symbol of post-war freedom. Kerouac seems to embody this momentum; the world and the burning spirit his work describes is a precursor to the sixties. His muse, Neal Cassady, is the common link—appearing as Dean Moriarty in Kerouac's first major work and later as himself in Wolfe's The Electric Kool-Aid Acid Test. My parents were a part of this westward yearning's last true surge in the early seventies, when they ventured cross-country and stayed out there for a time.
They'd caught the tail end of the wave, and told me a bit about it. I was full of stories, mostly fiction. Sweating in my twenty year old conversion van with a big friend, Ben—whose goals were less "literary"—I sought to recreate the legends I had read, the movies I had seen, and the tales my parents had told me. I was on a mission; I wanted my trip to measure up. Ben was on vacation. Our folly is chronicled within; three weeks and four thousand miles of it.M.F.A.
Masters
English
Arts and Sciences
40
Yaseen, Hogar M. "Generalized root graded Lie algebras." Thesis, University of Leicester, 2018. http://hdl.handle.net/2381/42765.
Full textAbstract:
Let g be a non-zero finite-dimensional split semisimple Lie algebra with root system Δ. Let Γ be a finite set of integral weights of g containing Δ and {0}. We say that a Lie algebra L over F is generalized root graded, or more exactly (Γ,g)-graded, if L contains a semisimple subalgebra isomorphic to g, the g-module L is the direct sum of its weight subspaces Lα (α ∈ Γ) and L is generated by all Lα with α ̸= 0 as a Lie algebra. If g is the split simple Lie algebra and Γ = Δ∪{0} then L is said to be root-graded. Let g∼= sln and Θn = {0,±εi±ε j,±εi,±2εi | 1 ≤ i ̸= j ≤ n} where {ε1, . . . , εn} is the set of weights of the natural sln-module. Then a Lie algebra L is (Θn,g)-graded if and only if L is generated by g as an ideal and the g-module L decomposes into copies of the adjoint module, the natural module V, its symmetric and exterior squares S2V and ∧2V, their duals and the one dimensional trivial g-module. In this thesis we study properties of generalized root graded Lie algebras and focus our attention on (Θn, sln)-graded Lie algebras. We describe the multiplicative structures and the coordinate algebras of (Θn, sln)-graded Lie algebras, classify these Lie algebras and determine their central extensions.
41
Roberts, Kieran. "Lie algebras and incidence geometry." Thesis, University of Birmingham, 2012. http://etheses.bham.ac.uk//id/eprint/3483/.
Full textAbstract:
An element \(\char{cmti10}{0x78}\) of a Lie algebra \(\char{cmmi10}{0x4c}\) over the field \(\char{cmmi10}{0x46}\) is extremal if [\(\char{cmti10}{0x78}\), [\(\char{cmti10}{0x78}\), \(\char{cmmi10}{0x4c}\)]] \(\subseteq\)\(\char{cmmi10}{0x46}\)\(\char{cmti10}{0x78}\). One can define the extremal geometry of \(\char{cmmi10}{0x4c}\) whose points \(\char{cmsy10}{0x45}\) are the projective points of extremal elements and lines \(\char{cmsy10}{0x46}\) are projective lines all of whose points belong to \(\char{cmsy10}{0x45}\). We prove that any finite dimensional simple Lie algebra \(\char{cmmi10}{0x4c}\) is a classical Lie algebra of type A\(_n\) if it satisfies the following properties: \(\char{cmmi10}{0x4c}\) contains no elements \(\char{cmti10}{0x78}\) such that [\(\char{cmti10}{0x78}\), [\(\char{cmti10}{0x78}\), \(\char{cmmi10}{0x4c}\)]] = 0, \(\char{cmmi10}{0x4c}\) is generated by its extremal elements and the extremal geometry \(\char{cmsy10}{0x45}\) of \(\char{cmmi10}{0x4c}\) is a root shadow space of type A\(_{n,(1,n)}\).
42
Caradot, Antoine. "Singularité et théorie de Lie." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSE1086/document.
Full textAbstract:
Soit Γ un sous-groupe fini de SU2(ℂ). Alors le quotient ℂ2/Γ peut être plongé dans ℂ3 sous la forme d'une surface munie d'une singularité isolée. Le quotient ℂ2/Γ est appelé singularité de Klein, d'après F. Klein qui fut le premier à les décrire en 1884. A travers leurs résolutions minimales, ces singularités ont un lien étroit avec les diagrammes de Dynkin simplement lacés de types Ar, Dr et Er. Dans les années 1970, E. Brieskorn et P. Slodowy ont tiré profit de cette connection pour décrire les résolutions et les déformations de ces singularités à l'aide de la théorie de Lie. En 1998 P. Slodowy et H. Cassens ont construit les déformations semiuniverselles des ℂ2/Γ à l'aide de la théorie des carquois ainsi que des travaux de P.B. Kronheimer en géométrie symplectique datant de 1989. En théorie de Lie, la classification des algèbres de Lie simples divisent ces dernières en deux classes: les algèbres de Lie de types Ar, Dr et Er qui sont simplement lacées, et celles de types Br, Cr, F4 et G2 appelées non-homogènes. A l'aide d'un second sous-groupe fini Γ' de SU2(ℂ) tel que Γ ⊲ Γ', P. Slodowy a étendu en 1978 la notion de singularité de Klein aux algèbres de Lie non-homogènes en ajoutant à ℂ2/Γ le groupe d'automorphismes Ω= Γ'/Γ du diagramme de Dynkin associé à la singularité. L'objectif de cette thèse est de généraliser la construction de H. Cassens et P. Slodowy à ces singularités de types Br, Cr, F4 et G2. Il en résultera des constructions explicites des déformations semiuniverselles de types inhomogènes sur les fibres desquelles le groupe Ω agit. Le passage au quotient d'une telle application révèle alors une déformation d'une singularité de type ℂ2/Γ'Let Γ be a finite subgroup of SU2(ℂ). Then the quotient ℂ2/Γ can be embedded in ℂ3 as a surface with an isolated singularity. The quotient ℂ2/Γ is called a Kleinian singularity, after F. Klein who studied them first in 1884. Through their minimal resolutions, these singularities have a deep connection with simply-laced Dynkin diagrams of types Ar, Dr and Er. In the 1970's E. Brieskorn and P. Slodowy took advantage of this connection to describe the resolutions and deformations of these singularities in terms of Lie theory. In 1998 P. Slodowy and H. Cassens constructed the semiuniversal deformations of the Kleinian singularities using quiver theory and work from 1989 by P.B. Kronheimer on symplectic geometry. In Lie theory, the classification of simple Lie algebras allows for a separation in two classes: those simply-laced of types Ar, Dr and Er, and those of types Br, Cr, F4 and G2 called inhomogeneous. With the use of a second finite subgroup Γ’ of SU2(ℂ) such that Γ ⊲ Γ’, P. Slodowy extended in 1978 the definition of a Kleinian singularity to the inhomogeneous types by adding to ℂ2/Γ the group of automorphisms Ω= Γ’/Γ of the Dynkin diagram associated to the singularity. The purpose of this thesis is to generalize H. Cassens' and P. Slodowy's construction to the singularities of types Br, Cr, F4 and G2. It will lead to explicit semiuniversal deformations of inhomogeneous types on the fibers of which the group Ω acts. By quotienting such a map we obtain a deformation of a singularity ℂ2/Γ’
43
Nilsson, Jonathan. "Simple Modules over Lie Algebras." Doctoral thesis, Uppsala universitet, Algebra och geometri, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-283061.
Full textAbstract:
Simple modules are the elemental components in representation theory for Lie algebras, and numerous mathematicians have worked on their construction and classification over the last century. This thesis consists of an introduction together with four research articles on the subject of simple Lie algebra modules. In the introduction we give a light treatment of the basic structure theory for simple finite dimensional complex Lie algebras and their representations. In particular we give a brief overview of the most well-known classes of Lie algebra modules: highest weight modules, cuspidal modules, Gelfand-Zetlin modules, Whittaker modules, and parabolically induced modules. The four papers contribute to the subject by construction and classification of new classes of Lie algebra modules. The first two papers focus on U(h)-free modules of rank 1 i.e. modules which are free of rank 1 when restricted to the enveloping algebra of the Cartan subalgebra. In Paper I we classify all such modules for the special linear Lie algebras sln+1(C), and we determine which of these modules are simple. For sl2 we also obtain some additional results on tensor product decomposition. Paper II uses the theory of coherent families to obtain a similar classification for U(h)-free modules over the symplectic Lie algebras sp2n(C). We also give a proof that U(h)-free modules do not exist for any other simple finite-dimensional algebras which completes the classification. In Paper III we construct a new large family of simple generalized Whittaker modules over the general linear Lie algebra gl2n(C). This family of modules is parametrized by non-singular nxn-matrices which makes it the second largest known family of gl2n-modules after the Gelfand-Zetlin modules. In Paper IV we obtain a new class of sln+2(C)-modules by applying the techniques of parabolic induction to the U(h)-free sln+1-modules we constructed in Paper I. We determine necessary and sufficient conditions for these parabolically induced modules to be simple.
44
Barton, Christine H. "Magic squares of Lie algebras." Thesis, University of York, 2000. http://etheses.whiterose.ac.uk/10884/.
Full text
45
Silva, Viviane Moretto da. "Algebras de Lie finitamente apresentaveis." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306934.
Full textAbstract:
Orientador: Dessislava Hristova KochloukovaDissertação (mestrado) - Universidade Estadual de Campinas. Instituto de Matematica, Estatistica e Computação Científica
Made available in DSpace on 2018-08-04T04:02:42Z (GMT). No. of bitstreams: 1 Silva_VivianeMorettoda_M.pdf: 772022 bytes, checksum: df78c072210885081ecac3c1e89b04fd (MD5) Previous issue date: 2005
Resumo: Nesta dissertação de mestrado, estudamos propriedades de álgebras de Lie. As Álgebras de Lie têm grande importância nao somente na teoria de álgebras não associativas, elas surgem também em geometria, topologia e no estudo da teoria de grupos por exemplo. As definições e resultados básicos sobre álgebras de Lie estão inclusos no Capítulo 2. Para esta parte do trabalho, utilizamos os livros [1] e [2]. O nosso enfoque foi sobre álgebras universais envelopantes, mergulhando assim a álgebra de Lie em álgebras associativas (Seções 2.4, 2.5 e 2.6). O objetivo principal da dissertação foi estudar o artigo [4], ¿Finite presentation of abelian-by-finite dimensional Lie algebras¿, que classifica álgebras de Lie finitamente apresentáveis (no sentido de serem definidas por número finito de geradores e relações) que são extensões de ideal abeliano por álgebra de Lie de dimensão finita. Definimos álgebras de Lie livres na seção 2.7.Tratam-se de objetos na categoria de álgebras de Lie que satisfazem propriedade universal semelhante a definição de grupos livres. A classificação de álgebras de Lie que são extensões de ideal abeliano por álgebra de Lie de dimensão finita usa teoria de módulos Noetherianos. No Capítulo 1 incluímos resultados básicos sobre módulos, em particular estudamos módulos Noetherianos, não necessariamente sobre anéis comutativos (para este estudo utilizamos [9]), embora alguns resultados sejam válidos somente no caso onde o anel básico é comutativo (caso do Teorema da Base de Hilbert 1.31 no Capítulo 1). No final, nos Capítulos 3 e 4, explicamos de maneira bem minuciosa (com mais 6 detalhes que o original) o resultado principal de [4], que 'e apresentado na página 42: Proposicão 3.2: Seja L uma álgebra de Lie finitamente gerada sobre o corpo K. Suponha que L tenha um ideal abeliano A tal que L/A tem dimensão finita como espaço vetorial. Seja R álgebra universal envelopante de L/A. Suponha também que o quadrado tensorial A X A é finitamente gerado como R-módulo sobre a ação diagonal. Então L é finitamente apresentável. Os métodos da demonstração de 3.2 envolvem muitos cálculos com relações em L para mostrar que um conjunto finito E 'e suficiente para gerar todas as relações em L. Embora os cálculos sejam muitos, a técnica principal 'e a indução e a Identidade de Jacobi. A teoria de módulos Noetherianos também foi muito utilizada
Abstract: In this work we study the classification of finitely presented abelian-by-finite dimensional Lie algebras given in [4]. If L is a Lie algebra, an extension of an abelian ideal A by a finite dimensional Lie algebra L/A then L is finitely presented if and only if A X A is finitely generated as U(L/A)-module via the diagonal action, where U(L/A) is the universal enveloping algebra of L/A. We study in detail the result that finite generation of A X A over U(L/A) implies finite presentability of L
Mestrado
Matematica
Mestre em Matemática
46
Oliveira, Leonardo Gomes. "Álgebras de Lie semi-simples." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-27052009-113224/.
Full textAbstract:
A dissertação tem como tema as álgebras de Lie. Especificamente álgebras de Lie semi-simples e suas propriedades . Para encontramos essas propriedades estudamos os conceitos básicos da teoria das álgebras de Lie e suas representações. Então fizemos a classificação dessas álgebras por diagramas de Dynkin explicitando quais os possíveis diagramas que são associados a uma álgebra de Lie semi-simples. Por fim, demonstramos vários resultados concernentes a essa classificação, dentre esses, o principal resultado demonstrado foi: os diagramas de Dynkin são um invariante completo das álgebras de Lie semi-simplesThe dissertation has the theme Lie algebras. Specifically semi-simple Lie algebras and its properties. To find these properties we studied the basic concepts of the theory of Lie algebras and their representations. Then we did the classification by Dynkin diagrams of these algebras and explaining the possible diagrams that are associated with a semi-simple Lie algebra. Finally, we demonstrate several results related to this classification, among these, the main result demonstrated was: the Dynkin diagrams are a complete invariant of semi-simple Lie algebras
47
Gilg, Marc. "Super-algèbres de Lie nilpotentes." Mulhouse, 2000. http://www.theses.fr/2000MULH0604.
Full textAbstract:
Dans ce travail, on s'intéresse aux propriétés et à la classification des super-algèbres de Lie nilpotentes. On les caractérise à l'aide des suites centrales puis en utilisant l'invariant de Goze, élargi aux super-algèbres de Lie nilpotentes. On y donne aussi la définition des super-algèbres de Lie filiformes et des propriétés générales concernant les super-algèbres de Lie nilpotentes. Dans la suite, les super-algèbres filiformes s'obtiennent par déformation linéaire d'une super-algèbre de Lie filiforme modèle, notée Ln,m. Ces déformations sont construites à partir des 2-cocycles paires de Ln,m, ce qui nous conduit à l'étude de ces cocycles. Du point de vue géométrique, on en déduit la dimension de l'orbite de Ln,m et une estimation de la dimension d'une composante irréductible contenant Ln,m dans la variété des super-algèbres de Lie nilpotentes. On établit, dans le dernier chapitre, la classification à isomorphisme près des super-algèbres de Lie filiformes dans les cas suivants : G = G0 ○+ G1 avec dim G0 = n + 1 et dim G1 = m où (n,m) ∈ {(1,m) ; (2,2) ; (2,3) ; (3,2) ; (4,2) ; (5,2)}.
48
Knibbeler, Vincent. "Invariants of automorphic Lie algebras." Thesis, Northumbria University, 2015. http://nrl.northumbria.ac.uk/23590/.
Full textAbstract:
Automorphic Lie Algebras arise in the context of reduction groups introduced in the late 1970s [35] in the field of integrable systems. They are subalgebras of Lie algebras over a ring of rational functions, denied by invariance under the action of a finite group, the reduction group. Since their introduction in 2005 [29, 31], mathematicians aimed to classify Automorphic Lie Algebras. Past work shows remarkable uniformity between the Lie algebras associated to different reduction groups. That is, many Automorphic Lie Algebras with nonisomorphic reduction groups are isomorphic [4, 30]. In this thesis we set out to find the origin of these observations by searching for properties that are independent of the reduction group, called invariants of Automorphic Lie Algebras. The uniformity of Automorphic Lie Algebras with nonisomorphic reduction groups starts at the Riemann sphere containing the spectral parameter, restricting the finite groups to the polyhedral groups. Through the use of classical invariant theory and the properties of this class of groups it is shown that Automorphic Lie Algebras are freely generated modules over the polynomial ring in one variable. Moreover, the number of generators equals the dimension of the base Lie algebra, yielding an invariant. This allows the definition of the determinant of invariant vectors which will turn out to be another invariant. A surprisingly simple formula is given expressing this determinant as a monomial in ground forms. All invariants are used to set up a structure theory for Automorphic Lie Algebras. This naturally leads to a cohomology theory for root systems. A first exploration of this structure theory narrows down the search for Automorphic Lie Algebras signicantly. Various particular cases are fully determined by their invariants, including most of the previously studied Automorphic Lie Algebras, thereby providing an explanation for their uniformity. In addition, the structure theory advances the classification project. For example, it clarifies the effect of a change in pole orbit resulting in various new Cartan-Weyl normal form generators for Automorphic Lie Algebras. From a more general perspective, the success of the structure theory and root system cohomology in absence of a field promises interesting theoretical developments for Lie algebras over a graded ring.
49
Topley, Lewis William. "Centralisers in classical Lie algebras." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/centralisers-in-classical-lie-algebras(4138e280-d893-443e-b7f2-c30855dc82ee).html.
Full textAbstract:
In this thesis we shall discuss some properties of centralisers in classical Lie algebas and related structures. Let K be an algebraically closed field of characteristic p greater than or equal to 0. Let G be a simple algebraic group over K. We shall denote by g = Lie(G) the Lie algebra of G, and for x in g denote by g_x the centraliser. Our results follow three distinct but related themes: the modular representation theory of centralisers, the sheets of simple Lie algebras and the representation theory of finite W-algebras and enveloping algebras. When G is of type A or C and p > 0 is a good prime for G, we show that the invariant algebras S(g_x)^{G_x} and U(g_x)^{G_x} and polynomial algebras on rank g generators, that the algebra S(g_x)^{g_x} is generated by S(g_x)^p and S(g_x)^{G_x}, whilst U(g_x)^{g_x} is generated by U(g_x)^{G_x} and the p-centre, generalising a classical theorem of Veldkamp. We apply the latter result to confirm the first Kac-Weisfeiler conjecture for g_x, giving a precise upper bound for the dimensions of simple U(g_x)-modules. This allows us to characterise the smooth locus of the Zassenhaus variety in algebraic terms. These results correspond to an article, soon to appear in the Journal of Algebra. The results of the next chapter are particular to the case x nilpotent with G connected of type B, C or D in any characteristic good for G. Our discussion is motivated by the theory of finite W-algebras which shall occupy our discussion in the final chapter, although we make several deductions of independent interest. We begin by describing a vector space decomposition for [g_x g_x] which in turn allows us to give a formula for dim g_x^\ab where g_x^\ab := g_x / [g_x g_x]. We then concoct a combinatorial parameterisation of the sheets of g containing x and use it to classify the nilpotent orbits lying in a unique sheet. We call these orbits non-singular. Subsequently we give a formula for the maximal rank of sheets containing x and show that it coincides with dim g_x^\ab if and only if x is non-singular. The latter result is applied to show for any (not necessarily nilpotent) x in g lying in a unique sheet, that the orthogonal complement to [g_x g_x] is the tangent space to the sheet, confirming a recent conjecture. In the final chapter we set p = 0 and consider the finite W-algebra U(g,x), again with G of type B, C or D. The one dimensional representations are parameterised by the maximal spectrum of the maximal abelian quotient E = Specm U(g, x)^\ab and we classify the nilpotent elements in classical types for which E is isomorphic to an affine space A^d_K: they are precisely the non-singular elements of the previous chapter. The component group acts naturally on E and the fixed point space lies in bijective correspondence with the set of primitive ideals of U(g) for which the multiplicity of the correspoding primitive quotient is one. We call them multiplicity free. We show that this fixed point space is always an affine space, and calculate its dimension. Finally we exploit Skryabin's equivalence to study parabolic induction of multiplicity free ideals. In particular we show that every multiplicity free ideals whose associated variety is the closure of an induced orbit is itself induced from a completely prime primitive ideals with nice properties, generalising a theorem of Moeglin. The results of the final two chapters make up a part of a joint work with Alexander Premet.
50
Castronuovo, Niccolò. "Gruppi e algebre di Lie." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2011. http://amslaurea.unibo.it/2447/.
Full text