On one class of extensions of Lie algebras and the Casimir functions related to it

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dc.contributor.advisorlanovsky, Alexandar
dc.contributor.authordos Santos, Moses Caires
dc.date.accessioned2024-04-11T13:30:38Z
dc.date.available2024-04-11T13:30:38Z
dc.date.issued2009
dc.date.updated2024-04-11T13:03:49Z
dc.description.abstractIn chapter 1, we introduce the extensions and cohomologies of Lie algebras, followed by the lemmas of Vhitehcad and finally the Levi-decomposition theorem. In chapter 2, we introduce the "universal" extensions of the Lie algebras as originally given in [l] and classify them up to some point (where n::::; 4 as given in (l]). In Chapter 3, an alternative approach to these "universal" extensions is given, that seen in [2] and the t·wo approaches are compared and finally; In Chapter 4, the related Casimir Invariants are introduced. We attempt to further understand their algebraic properties developing the ideas of [l] and [2]. In the appendices we give some additional information that is needed to understand the text.
dc.identifier.apacitationdos Santos, M. C. (2009). <i>ETD: On one class of extensions of Lie algebras and the Casimir functions related to it</i>. (). ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/39363en_ZA
dc.identifier.chicagocitationdos Santos, Moses Caires. <i>"ETD: On one class of extensions of Lie algebras and the Casimir functions related to it."</i> ., ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2009. http://hdl.handle.net/11427/39363en_ZA
dc.identifier.citationdos Santos, M.C. 2009. ETD: On one class of extensions of Lie algebras and the Casimir functions related to it. . ,Faculty of Science ,Department of Mathematics and Applied Mathematics. http://hdl.handle.net/11427/39363en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - dos Santos, Moses Caires AB - In chapter 1, we introduce the extensions and cohomologies of Lie algebras, followed by the lemmas of Vhitehcad and finally the Levi-decomposition theorem. In chapter 2, we introduce the "universal" extensions of the Lie algebras as originally given in [l] and classify them up to some point (where n::::; 4 as given in (l]). In Chapter 3, an alternative approach to these "universal" extensions is given, that seen in [2] and the t·wo approaches are compared and finally; In Chapter 4, the related Casimir Invariants are introduced. We attempt to further understand their algebraic properties developing the ideas of [l] and [2]. In the appendices we give some additional information that is needed to understand the text. DA - 2009 DB - OpenUCT DP - University of Cape Town KW - Applied Mathematics LK - https://open.uct.ac.za PY - 2009 T1 - ETD: On one class of extensions of Lie algebras and the Casimir functions related to it TI - ETD: On one class of extensions of Lie algebras and the Casimir functions related to it UR - http://hdl.handle.net/11427/39363 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/39363
dc.identifier.vancouvercitationdos Santos MC. ETD: On one class of extensions of Lie algebras and the Casimir functions related to it. []. ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2009 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/39363en_ZA
dc.language.rfc3066eng
dc.publisher.departmentDepartment of Mathematics and Applied Mathematics
dc.publisher.facultyFaculty of Science
dc.subjectApplied Mathematics
dc.titleOn one class of extensions of Lie algebras and the Casimir functions related to it
dc.typeThesis / Dissertation
dc.type.qualificationlevelMasters
dc.type.qualificationlevelMasters
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