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On one class of extensions of Lie algebras and the Casimir functions related to it
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...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2024
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| _version_ | 1867613153767981056 |
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| access_status_str | Open Access |
| author | dos Santos, Moses Caires |
| author2 | lanovsky, Alexandar |
| author_browse | dos Santos, Moses Caires lanovsky, Alexandar |
| author_facet | lanovsky, Alexandar dos Santos, Moses Caires |
| author_sort | dos Santos, Moses Caires |
| collection | Thesis |
| description | 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. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/39363 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:35.974Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/39363 On one class of extensions of Lie algebras and the Casimir functions related to it dos Santos, Moses Caires lanovsky, Alexandar Applied Mathematics 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. 2024-04-11T13:30:38Z 2024-04-11T13:30:38Z 2009 2024-04-11T13:03:49Z Thesis / Dissertation Masters Masters http://hdl.handle.net/11427/39363 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science |
| spellingShingle | Applied Mathematics dos Santos, Moses Caires On one class of extensions of Lie algebras and the Casimir functions related to it |
| thesis_degree_str | Master's |
| title | On one class of extensions of Lie algebras and the Casimir functions related to it |
| title_full | On one class of extensions of Lie algebras and the Casimir functions related to it |
| title_fullStr | On one class of extensions of Lie algebras and the Casimir functions related to it |
| title_full_unstemmed | On one class of extensions of Lie algebras and the Casimir functions related to it |
| title_short | On one class of extensions of Lie algebras and the Casimir functions related to it |
| title_sort | on one class of extensions of lie algebras and the casimir functions related to it |
| topic | Applied Mathematics |
| url | http://hdl.handle.net/11427/39363 |
| work_keys_str_mv | AT dossantosmosescaires ononeclassofextensionsofliealgebrasandthecasimirfunctionsrelatedtoit |