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Dissertations / Theses on the topic 'Lie'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

Eddy, Scott M. "Lie Groups and Lie Algebras." Youngstown State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1320152161.

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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.

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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.

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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/.

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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 te

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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.

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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.

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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).<br>Liegrupper kan ses som grupper som även är glatta. Målet med den här rapporten är att definiera Lie

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7

Aminou, Adérodjou A. Rachidi. "Groupes de Lie-Poisson et bigèbres de Lie." Lille 1, 1988. http://www.theses.fr/1988LIL10139.

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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 q

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8

Aminou, Adérodjou A. Rachidi. "Groupes de Lie-Poisson et bigèbres de Lie." Grenoble 2 : ANRT, 1988. http://catalogue.bnf.fr/ark:/12148/cb37611312n.

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9

Höglund, Joel. "Lie-algebror." Thesis, Uppsala universitet, Algebra och geometri, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-202056.

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10

Mihaylishin, P. A. "Lie detector." Thesis, Сумський державний університет, 2012. http://essuir.sumdu.edu.ua/handle/123456789/28533.

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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.

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12

Traustason, Gunnar. "Engel Lie algebras." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334292.

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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/.

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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 alg

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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.

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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

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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/.

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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.<br>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 cohomo

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16

Remm, Elisabeth. "Structures affines sur les algébres de Lie et opérades Lie admissibles." Mulhouse, 2001. http://www.theses.fr/2001MULH0670.

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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 muni

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17

Duong, Minh thanh. "A new invariant of quadratic lie algebras and quadratic lie superalgebras." Thesis, Dijon, 2011. http://www.theses.fr/2011DIJOS021/document.

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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’ex

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18

Ben, Abdeljelil Amine. "Generalized Derivations of Ternary Lie Algebras and n-BiHom-Lie Algebras." Scholar Commons, 2019. https://scholarcommons.usf.edu/etd/7743.

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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-de

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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.

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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.

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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.

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21

Bagnoli, Lucia. "Z-graded Lie superalgebras." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/14118/.

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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.

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22

Williams, Michael Peretzian. "Nilpotent N-Lie Algebras." NCSU, 2004. http://www.lib.ncsu.edu/theses/available/etd-02162004-083708/.

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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.

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23

Levene, Rupert Howard. "Lie semigroup operator algebras." Thesis, Lancaster University, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.421841.

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24

Street, C. N. H. "Lie detection : cognitive processes." Thesis, University College London (University of London), 2013. http://discovery.ucl.ac.uk/1414942/.

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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

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25

Lacerda, Conrado Damato de 1986. "Grupos de Lie compactos." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305808.

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Orientador: Luiz Antonio Barrera San Martin<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>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<br>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<br>Abstract: In this work we present the main results about comp

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26

Almeida, Luis Roberto Lucinger de 1983. "Simetrias de Lie estocásticas." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306332.

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Orientador: Pedro José Catuogno<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>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<br>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 u

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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.

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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'équ

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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.

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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.

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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.

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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 l

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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.

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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 ab

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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.

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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 wo

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33

Jimenez, William. "Riemannian submersions and Lie groups." College Park, Md. : University of Maryland, 2005. http://hdl.handle.net/1903/2648.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2005.<br>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.

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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.

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35

Furutsu, Hirotoshi. "Representations of Lie Superalgebras, II." 京都大学 (Kyoto University), 1991. http://hdl.handle.net/2433/168802.

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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<br>Kyoto University (京都大学)<br>0048<br>新制・課程博士<br>理学博士<br>甲第4695号<br>理博第1293号<br>新制||理||720(附属図書館)<br>UT51-91-E66<br>京都大学大学院理学研究科数学専攻<br>(主査)教授平井武, 教授池部晃生, 教授岩崎敷久<br>学位規則第5条第1項該当

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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.

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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.<br>The

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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.

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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.

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38

Brodzki, Jacek. "Cyclic cohomology and Lie cochains." Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.257657.

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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.

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"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 Ca

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40

Yaseen, Hogar M. "Generalized root graded Lie algebras." Thesis, University of Leicester, 2018. http://hdl.handle.net/2381/42765.

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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} i

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41

Roberts, Kieran. "Lie algebras and incidence geometry." Thesis, University of Birmingham, 2012. http://etheses.bham.ac.uk//id/eprint/3483/.

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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}{0

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42

Caradot, Antoine. "Singularité et théorie de Lie." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSE1086/document.

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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. Slod

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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.

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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 modul

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44

Barton, Christine H. "Magic squares of Lie algebras." Thesis, University of York, 2000. http://etheses.whiterose.ac.uk/10884/.

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Silva, Viviane Moretto da. "Algebras de Lie finitamente apresentaveis." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306934.

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Orientador: Dessislava Hristova Kochloukova<br>Dissertação (mestrado) - Universidade Estadual de Campinas. Instituto de Matematica, Estatistica e Computação Científica<br>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<br>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 est

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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/.

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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 s

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47

Gilg, Marc. "Super-algèbres de Lie nilpotentes." Mulhouse, 2000. http://www.theses.fr/2000MULH0604.

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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,

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Knibbeler, Vincent. "Invariants of automorphic Lie algebras." Thesis, Northumbria University, 2015. http://nrl.northumbria.ac.uk/23590/.

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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

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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.

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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

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Castronuovo, Niccolò. "Gruppi e algebre di Lie." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2011. http://amslaurea.unibo.it/2447/.

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