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Dissertations / Theses on the topic 'Group algebras; Symmetry'

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Published: 4 June 2021

Last updated: 1 February 2022

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1

Hills, Robert K. "The algebra of a class of permutation invariant irreducible operators." Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.260729.

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2

Moreira, Rodriguez Rivera Walter. "Products of representations of the symmetric group and non-commutative versions." Texas A&M University, 2008. http://hdl.handle.net/1969.1/85938.

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We construct a new operation among representations of the symmetric group that interpolates between the classical internal and external products, which are defined in terms of tensor product and induction of representations. Following Malvenuto and Reutenauer, we pass from symmetric functions to non-commutative symmetric functions and from there to the algebra of permutations in order to relate the internal and external products to the composition and convolution of linear endomorphisms of the tensor algebra. The new product we construct corresponds to the Heisenberg product of endomorphisms o

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3

Hill, David Edward. "The Jantzen-Shapovalov form and Cartan invariants of symmetric groups and Hecke algebras /." view abstract or download file of text, 2007. http://proquest.umi.com/pqdweb?did=1400959351&sid=1&Fmt=2&clientId=11238&RQT=309&VName=PQD.

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Thesis (Ph. D.)--University of Oregon, 2007.<br>Typescript. Includes vita and abstract. Includes bibliographical references (leaves 107-108). Also available for download via the World Wide Web; free to University of Oregon users.

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4

Han, Gang. "Clifford algebras associated with symmetric pairs /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?MATH%202004%20HAN.

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5

Tan, Kai Meng. "Small defect blocks of symmetric group algebras." Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624153.

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6

Ruff, Oliver. "Completely splittable representations of symmetric groups and affine Hecke algebras /." view abstract or download file of text, 2005. http://wwwlib.umi.com/cr/uoregon/fullcit?p3190545.

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Thesis (Ph. D.)--University of Oregon, 2005.<br>Typescript. Includes vita and abstract. Includes bibliographical references (leaves 44-45). Also available for download via the World Wide Web; free to University of Oregon users.

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7

Fayers, Matthew. "Representations of symmetric groups and Schur algebras." Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.620642.

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8

Abubakar, Ahmed Bello. "The structure of symmetric group algebras at arbitrary characteristic." Thesis, University of East London, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.300326.

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9

Zwicknagl, Sebastian. "Equivariant Poisson algebras and their deformations /." view abstract or download file of text, 2006. http://proquest.umi.com/pqdweb?did=1280144671&sid=2&Fmt=2&clientId=11238&RQT=309&VName=PQD.

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Thesis (Ph. D.)--University of Oregon, 2006.<br>Typescript. Includes vita and abstract. "In this dissertation I investigate Poisson structures on symmetric and exterior algebras of modules over complex reductive Lie algebras. I use the results to study the braided symmetric and exterior algebras"--P. 1. Includes bibliographical references (leaves 150-152). Also available for download via the World Wide Web; free to University of Oregon users.

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10

Manriquez, Adam. "Symmetric Presentations, Representations, and Related Topics." CSUSB ScholarWorks, 2018. https://scholarworks.lib.csusb.edu/etd/711.

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The purpose of this thesis is to develop original symmetric presentations of finite non-abelian simple groups, particularly the sporadic simple groups. We have found original symmetric presentations for the Janko group J1, the Mathieu group M12, the Symplectic groups S(3,4) and S(4,5), a Lie type group Suz(8), and the automorphism group of the Unitary group U(3,5) as homomorphic images of the progenitors 2*60 : (2 x A5), 2*60 : A5, 2*56 : (23 : 7), and 2*28 : (PGL(2,7):2), respectively. We have also discovered the groups 24 : A5, 34 : S5, PSL(2,31), PSL(2,11), PSL(2,19), PSL(2,41), A8, 34 : S5

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11

Paget, Rowena. "Representation theory of symmetric groups and related algebras." Thesis, University of Oxford, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.270235.

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12

Krawzik, Naomi. "Graded Hecke Algebras for the Symmetric Group in Positive Characteristic." Thesis, University of North Texas, 2020. https://digital.library.unt.edu/ark:/67531/metadc1707315/.

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Graded Hecke algebras are deformations of skew group algebras which arise from a group acting on a polynomial ring. Over fields of characteristic zero, these deformations have been studied in depth and include both symplectic reflection algebras and rational Cherednik algebras as examples. In Lusztig's graded affine Hecke algebras, the action of the group is deformed, but not the commutativity of the vectors. In Drinfeld's Hecke algebras, the commutativity of the vectors is deformed, but not the action of the group. Lusztig's algebras are all isomorphic to Drinfeld's algebras in the nonmodu

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13

Ault, Shaun V. "On the Symmetric Homology of Algebras." The Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1218237992.

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14

Bogdanic, Dusko. "Graded blocks of group algebras." Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:faeaaeab-1fe6-46a9-8cbb-f3f633131a73.

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In this thesis we study gradings on blocks of group algebras. The motivation to study gradings on blocks of group algebras and their transfer via derived and stable equivalences originates from some of the most important open conjectures in representation theory, such as Broue’s abelian defect group conjecture. This conjecture predicts the existence of derived equivalences between categories of modules. Some attempts to prove Broue’s conjecture by lifting stable equivalences to derived equivalences highlight the importance of understanding the connection between transferring gradings via stabl

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15

Yu, Jun. "Symmetric subgroups of automorphism groups of compact simple Lie algebras /." View abstract or full-text, 2009. http://library.ust.hk/cgi/db/thesis.pl?MATH%202009%20YU.

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16

Wickramasekara, Sujeewa, and sujeewa@physics utexas edu. "Symmetry Representations in the Rigged Hilbert Space Formulation of." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi993.ps.

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17

Penrod, Keith. "Infinite product groups /." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1977.pdf.

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18

Franjou, Vincent. "Modules et algebres instables sur l'algebre de steenrod : une etude aux nilpotents pres." Nantes, 1988. http://www.theses.fr/1988NANT2003.

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L'algebre de cohomologie modulo 2 d'un espace est un module instable sur l'algebre de steenrod a. Le premier chapitre etudie la categorie abelienne obtenue comme quotient de la categorie des a-modules instables par sa sous-categorie des a-modules nilpotents. On definit d'abord une notion de poids qui induit une filtration naturelle sur tout a-module instable. Cela nous permet de classifier les objets simples par les representations modulaires simples des groupes symetriques. La cohomologie des classifiants des 2-groupes abeliens elementaires est etudiee en exemple. On obtient aussi que notre c

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19

Kessar, Radha. "Blocks and source algebras for the double covers of the symmetric groups /." The Ohio State University, 1995. http://rave.ohiolink.edu/etdc/view?acc_num=osu148786754173406.

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20

Whitehouse, Sarah Ann. "Gamma (co)homology of commutative algebras and some related representations of the symmetric group." Thesis, University of Warwick, 1994. http://wrap.warwick.ac.uk/4214/.

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This thesis covers two related subjects: homology of commutative algebras and certain representations of the symmetric group. There are several different formulations of commutative algebra homology, all of which are known to agree when one works over a field of characteristic zero. During 1991-1992 my supervisor, Dr. Alan Robinson, motivated by homotopy-theoretic ideas, developed a new theory, Γ-homology [Rob, 2]. This is a homology theory for commutative rings, and more generally rings commutative up to homotopy. We consider the algebraic version of the theory. Chapter I covers background ma

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21

Winarski, Rebecca R. "Symmetry, isotopy, and irregular covers." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51868.

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We say that a covering space of the surface S over X has the Birman--Hilden property if the subgroup of the mapping class group of X consisting of mapping classes that have representatives that lift to S embeds in the mapping class group of S modulo the group of deck transformations. We identify one necessary condition and one sufficient condition for when a covering space has this property. We give new explicit examples of irregular branched covering spaces that do not satisfy the necessary condition as well as explicit covering spaces that satisfy the sufficient condition. Our criteria are c

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22

Nash, David A. 1982. "Graded representation theory of Hecke algebras." Thesis, University of Oregon, 2010. http://hdl.handle.net/1794/10871.

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xii, 76 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.<br>We study the graded representation theory of the Iwahori-Hecke algebra, denoted by Hd , of the symmetric group over a field of characteristic zero at a root of unity. More specifically, we use graded Specht modules to calculate the graded decomposition numbers for Hd . The algorithm arrived at is the Lascoux-Leclerc-Thibon algorithm in disguise. Thus we interpret the algorithm in terms of graded representation theory. We then use the algorithm

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23

Penrod, Keith G. "Infinite Product Group." BYU ScholarsArchive, 2007. https://scholarsarchive.byu.edu/etd/976.

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The theory of infinite multiplication has been studied in the case of the Hawaiian earring group, and has been seen to simplify the description of that group. In this paper we try to extend the theory of infinite multiplication to other groups and give a few examples of how this can be done. In particular, we discuss the theory as applied to symmetric groups and braid groups. We also give an equivalent definition to K. Eda's infinitary product as the fundamental group of a modified wedge product.

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24

Black, Samson 1979. "Representations of Hecke algebras and the Alexander polynomial." Thesis, University of Oregon, 2010. http://hdl.handle.net/1794/10847.

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viii, 50 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.<br>We study a certain quotient of the Iwahori-Hecke algebra of the symmetric group Sd , called the super Temperley-Lieb algebra STLd. The Alexander polynomial of a braid can be computed via a certain specialization of the Markov trace which descends to STLd. Combining this point of view with Ocneanu's formula for the Markov trace and Young's seminormal form, we deduce a new state-sum formula for the Alexander polynomial. We also give a direct combi

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25

Grindstaff, Dustin J. "Symmetric Presentations and Generation." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/202.

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The aim of this thesis is to generate original symmetric presentations for finite non-abelian simple groups. We will discuss many permutation progenitors, including but not limited to 2*14 : D28, 2∗9 : 3•(32), 3∗9 : 3•(32), 2∗21 : (7X3) : 2 as well as monomial progenitors, including 7∗5 :m A5, 3∗5 :m S5. We have included their homomorphic images which include the Mathieu group M12, 2•J2, 2XS(4, 5), as well as, many PGL′s, PSL′s and alternating groups. We will give proofs of the isomorphism types of each progenitor, either by hand using double coset enumeration or computer based using MAGMA. We

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26

Lamp, Leonard B. "SYMMETRIC PRESENTATIONS OF NON-ABELIAN SIMPLE GROUPS." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/222.

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The goal of this thesis is to show constructions of some of the sporadic groups such as the Mathieu group, M12, J1, Projective Special Linear groups, PSL(2,8), and PSL(2,11), Unitary group U(3,3) and many other non-abelian simple groups. Our purpose is to find all simple non-abelian groups as homomorphic images of permutation or monomial progenitors, as well grasping a deep understanding of group theory and extension theory to determine groups up to isomorphisms. The progenitor, developed by Robert T. Curtis, is a semi-direct product of the following form: P≅2*n: N = {πw | π ∈ N, w a reduced w

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27

Jones, Philip Robert. "Homology from posets." Thesis, University of East Anglia, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302072.

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28

Wasserman, Benjamin. "Variétés magnifiques de rang deux." Grenoble 1, 1997. http://www.theses.fr/1997GRE10037.

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Soit g un groupe reductif complexe (connexe). Les g-varietes magnifiques les plus connues sont celles de rang zero, a savoir les varietes de drapeaux generalisees g/p, celles de rang un, classifiees par akhiezer, et certaines varietes symetriques completes decrites par de concini et procesi comme par exemple le celebre espace des coniques completes. Il y a recemment un interet renouvele pour les varietes magnifiques de rang deux car des travaux de luna, brion, pauer et knop montrent que celles-ci jouent un role clef dans la theorie des varietes spheriques. L'objectif de ce travail est la class

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29

Pedone, M. (Matteo). "Algebraic methods for constructing blur-invariant operators and their applications." Doctoral thesis, Oulun yliopisto, 2015. http://urn.fi/urn:isbn:9789526208770.

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Abstract Image acquisition devices are always subject to physical limitations that often manifest as distortions in the appearance of the captured image. The most common types of distortions can be divided into two categories: geometric and radiometric distortions. Examples of the latter ones are: changes in brightness, contrast, or illumination, sensor noise and blur. Since image blur can have many different causes, it is usually not convenient and also computationally expensive to develop ad hoc algorithms to correct each specific type of blur. Instead, it is often possible to extract a blur

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30

at, Andreas Cap@esi ac. "Equivariant Symplectic Geometry of Cotangent Bundles." Moscow Math. J. 1, No.2 (2001) 287-299, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi996.ps.

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31

Chassaniol, Arthur. "Contributions à l'étude des groupes quantiques de permutations." Thesis, Clermont-Ferrand 2, 2016. http://www.theses.fr/2016CLF22709/document.

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Dans cette thèse nous étudions le groupe quantique d’automorphismes des graphes finis, introduit par Banica et Bichon. Dans un premier temps nous montrerons un théorème de structure du groupe quantique d’automorphismes du produit lexicographique de deux graphes finis réguliers, qui généralise un résultat classique de Sabidussi. Ce théorème donne une condition nécessaire et suffisante pour que ce groupe quantique s’exprime comme le produit en couronne libre des groupes quantiques d’automorphismes de ces deux graphes. Dans un deuxième temps, nous expliciterons certaines améliorations de résultat

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Fonseca, Marlon Pimenta. "Representações dos grupos simétrico e alternante e aplicações às identidades polinomiais." Universidade Federal de São Carlos, 2014. https://repositorio.ufscar.br/handle/ufscar/5912.

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Made available in DSpace on 2016-06-02T20:28:31Z (GMT). No. of bitstreams: 1 6450.pdf: 757192 bytes, checksum: 765b66ca6aed0686ecbcd10c145cefac (MD5) Previous issue date: 2014-11-28<br>Financiadora de Estudos e Projetos<br>In this dissertation we ll present a discussion about the Representations of the Symmetric Group Sn and Alternating Group An. We ll study basics results of the Young s Theory about the representations of the Symmetric Group and discover the decomposition of the algebra FSn in simple subalgebras. After, we ll utilize this decomposition to find the decomposition of the algeb

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33

Gilliers, Nicolas. "Non-commutative gauge symmetry and pseudo-unitary diffusions." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS113.

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Cette thèse est consacrée à l’étude de deux questions très différentes, reliées par les outils que nous utilisons pour les étudier. La première question est celle de la définition des théories de jauge sur un réseau avec un groupe de structure non commutatif. Ici, non commutatif ne signifie pas non Abelian, mais plutôt non commutatif au sens général de la géométrie non commutative. La deuxième question est celle du comportement des diffusions Browniennes sur des groupes matriciels non compacts d’un type spécifique, à savoir des groupes de matrices pseudo-orthogonales, pseudo-unitaires ou pseud

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Junior, Fernando Martins Antoneli. "Subalgebras maximais das álgebras de Lie semisimples, quebra de simetria e o código genético." Universidade de São Paulo, 1998. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-01092009-171526/.

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O propósito deste trabalho é dar uma contribuição ao projeto iniciado por Hornos & Hornos que visa explicar as degenerescências do código genético como resultado de sucessivas quebras de simetria ocorridas durante sua evolução. O modelo matemático usado requer a construção de todas as representações irredutíveis de dimensão 64 das álgebras de Lie simples (chamadas representações de códons) e a análise de suas regras de ramicação sob redução a subalgebras. A classicação de todas as possibilidades é baseada na classicação das subalgebras maximais das álgebras de Lie semisimples obtida por Dynkin

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35

Juršėnas, Rytis. "Algebraic development of many-body perturbation theory in theoretical atomic spectroscopy." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2010. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2010~D_20101223_153004-84982.

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The principal goals of the thesis are subjected to general methods and forms of effective operators by the nowadays demands of theoretical application of many-body perturbation theory to atomic physics. The present theoretical research follows up step by step by systematic observation of various possibilities to restrict the Fock space operators to their irreducible subspaces and the classification of irreducible tensor operators which represent the physical as well as the effective interactions. To ground the results of the thesis, the symbolic preparation of obtained expressions is strictly

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Santos, Laercio Jose dos. "Semigrupos gerados por classes laterais e funções caracteristicas de semigrupos." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305821.

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Orientador: Luiz Antonio Barrera San Martin<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-10T09:55:18Z (GMT). No. of bitstreams: 1 Santos_LaercioJosedos_D.pdf: 632399 bytes, checksum: 25069afc192f7633f7f8cd6bdce8e96e (MD5) Previous issue date: 2007<br>Resumo: Este trabalho divide-se em duas partes. Na primeira parte, obtemos condições necessárias e suficientes para que uma família de classes laterais de um subgrupo de Lie gere um subsemigrupo com interior não vazio. Aplicamos essas

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37

Pons, Viviane. "Combinatoire algébrique liée aux ordres sur les permutations." Phd thesis, Université Paris-Est, 2013. http://tel.archives-ouvertes.fr/tel-00952773.

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Cette thèse se situe dans le domaine de la combinatoire algébrique et porte sur l'étude et les applications de trois ordres sur les permutations : les deux ordres faibles (gauche et droit) et l'ordre fort ou de Bruhat. Dans un premier temps, nous étudions l'action du groupe symétrique sur les polynômes multivariés. En particulier, les opérateurs de emph{différences divisées} permettent de définir des bases de l'anneau des polynômes qui généralisent les fonctions de Schur aussi bien du point de vue de leur construction que de leur interprétation géométrique. Nous étudions plus particulièrement

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Thibault, de Chanvalon Manon. "Groupes quantiques : actions sur des modules hilbertiens et calculs différentiels." Thesis, Clermont-Ferrand 2, 2014. http://www.theses.fr/2014CLF22521/document.

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Gerber, Thomas. "Matrices de décomposition des algèbres d'Ariki-Koike et isomorphismes de cristaux dans les espaces de Fock." Phd thesis, Université François Rabelais - Tours, 2014. http://tel.archives-ouvertes.fr/tel-01057480.

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Cette thèse est consacrée à l'étude des représentations modulaires des algèbres d'Ariki-Koike, et des liens avec la théorie des cristaux et des bases canoniques de Kashiwara via le théorème de catégorification d'Ariki. Dans un premier temps, on étudie, grâce à des outils combinatoires, les matrices de décomposition de ces algèbres en généralisant les travaux de Geck et Jacon. On classifie entièrement les cas d'existence et de non-existence d'ensembles basiques, en construisant explicitement ces ensembles lorsqu'ils existent. On explicite ensuite les isomorphismes de cristaux pour les représent

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Delcroix-Oger, Bérénice. "Hyperarbres et Partitions semi-pointées : aspects combinatoires, algébriques et homologiques." Thesis, Lyon 1, 2014. http://www.theses.fr/2014LYO10243/document.

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Cette thèse est consacrée à l’étude combinatoire, algébrique et homologique des hyperarbres et des partitions semi-pointées. Nous étudions plus précisément des structures algébriques et homologiques construites à partir des hyperarbres, puis des partitions semi-pointées.Après un bref rappel des notions utilisées, nous utilisons la théorie des espèces de structure afin de déterminer l’action du groupe symétrique sur l’homologie du poset des hyperarbres. Cette action s’identifie à l’action du groupe symétrique liée à la structure anti-cyclique de l’opérade PreLie. Nous raffinons ensuite nos calc

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Gomez, John Hermes Castillo. "Propriedades de Lie de elementos simétricos sob involuções orientadas em álgebras de grupo." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-04012013-170011/.

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Sejam $F$ um corpo de característica diferente de $2$ e $G$ um grupo. A partir da involução clássica, que envia cada elemento em seu inverso, e uma orientação do grupo $G$ é possível definir uma involução clássica orientada na álgebra de grupo $FG$. O objetivo desta tese é estudar propriedades de Lie do conjunto dos elementos simétricos $(FG)^+$ e, em alguns casos, do conjunto dos elementos anti-simétricos $(FG)^-$. Primeiro, abordamos o caso quando $G$ não tem elementos de ordem $2$. Aqui, mostramos que se $(FG)^+$ (ou $(FG)^-$) é Lie nilpotente ou Lie $n$-Engel, então $FG$ também é Lie nilp

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McDermott, Matthew. "Fast Algorithms for Analyzing Partially Ranked Data." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/58.

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Imagine your local creamery administers a survey asking their patrons to choose their five favorite ice cream flavors. Any data collected by this survey would be an example of partially ranked data, as the set of all possible flavors is only ranked into subsets of the chosen flavors and the non-chosen flavors. If the creamery asks you to help analyze this data, what approaches could you take? One approach is to use the natural symmetries of the underlying data space to decompose any data set into smaller parts that can be more easily understood. In this work, I describe how to use permutation

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Wills, Luis Alberto. "Finite group graded lie algebraic extensions and trefoil symmetric relativity, standard model, yang mills and gravity theories." Thesis, 2008. http://hdl.handle.net/10125/11725.

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Mode of access: World Wide Web.<br>Thesis (Ph. D.)--University of Hawaii at Manoa, 2004.<br>Includes bibliographical references (leaves 159-164).<br>Electronic reproduction.<br>Also available by subscription via World Wide Web<br>x, 164 leaves, bound ill. 29 cm

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Shakalli, Tang Jeanette. "Deformations of Quantum Symmetric Algebras Extended by Groups." Thesis, 2012. http://hdl.handle.net/1969.1/ETD-TAMU-2012-05-10855.

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The study of deformations of an algebra has been a topic of interest for quite some time, since it allows us to not only produce new algebras but also better understand the original algebra. Given an algebra, finding all its deformations is, if at all possible, quite a challenging problem. For this reason, several specializations of this question have been proposed. For instance, some authors concentrate their efforts in the study of deformations of an algebra arising from an action of a Hopf algebra. The purpose of this dissertation is to discuss a general construction of a deformation of a

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Zimba, Kenneth. "Fischer-Clifford matrices of the generalized symmetric group and some associated groups." Thesis, 2005. http://hdl.handle.net/10413/1688.

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With the classification of finite simple groups having been completed in 1981, recent work in group theory has involved the study of the structures of simple groups. The character tables of maximal subgroups of simple groups give substantive information about these groups. Most of the maximal subgroups of simple groups are of extension type. Some of the maximal subgroups of simple groups contain constituents of the generalized symmetric groups. Here we shall be interested in discussing such groups which we may call groups associated with the generalized symmetric groups. There are several well

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Tysse, Jill Elizabeth. "The centers of spin symmetric and spin hyperoctahedral group algebras /." 2008. http://wwwlib.umi.com/dissertations/fullcit/3322506.

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Verma, Abhinav. "Irreducible Representations Of The Symmetric Group And The General Linear Group." Thesis, 2011. http://etd.iisc.ernet.in/handle/2005/1909.

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Representation theory is the study of abstract algebraic structures by representing their elements as linear transformations or matrices. It provides a bridge between the abstract symbolic mathematics and its explicit applications in nearly every branch of mathematics. Combinatorial representation theory aims to use combinatorial objects to model representations, thus answering questions in this ﬁeld combinatorially. Combinatorial objects are used to help describe, count and generate representations. This has led to a rich symbiotic relationship where combinatorics has helped answer algebraic

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Bashe, Mantombi Beryl. "Equivalence and symmetry groups of a nonlinear equation in plasma physics." Thesis, 2016. http://hdl.handle.net/10539/20598.

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Degree awarded with distinction on 6 December 1995. A research report submitted to the Faculty of Science, University of the Witwatersrand, in fulfilment of the requirements for the degree of Masters. Johannesburg, 1995.<br>In this work we give a brief overview of the existing group classification methods of partial differential equations by means of examples. On top of these methods we introduce another new method which classify according to low-dimensional Lie elgebras, One can ask: What is the aim of introducing a new method whilst there are existing methods? This question is answere

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Lemmer, Ryan Lee. "The paradigms of mechanics : a symmetry based approach." Thesis, 1996. http://hdl.handle.net/10413/4899.

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An overview of the historical developments of the paradigms of classical mechanics, the free particle, oscillator and the Kepler problem, is given ito (in terms of) their conserved quantities. Next, the orbits of the three paradigms are found from quadratic forms. The quadratic forms are constructed using first integrals found by the application of Poisson's theorem. The orbits are presented ito expanding surfaces defined by the quadratic forms. The Lie and Noether symmetries of the paradigms are investigated. The free particle is discussed in detail and an overview of the work done on the osc

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Pantazi, Hara. "First integrals for the Bianchi universes : supplementation of the Noetherian integrals with first integrals obtained by using Lie symmetries." 1997. http://hdl.handle.net/10413/5103.

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