{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/39363"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/39363","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"On one class of extensions of Lie algebras and the Casimir functions related to it","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["dos Santos, Moses Caires"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["lanovsky, Alexandar"],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009","date_published":"2009","updated_at":"2026-07-24T01:34:16Z","subjects":["Applied Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/39363","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["lanovsky, Alexandar"]},{"key":"dc:creator","label":"Author","values":["dos Santos, Moses Caires"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-04-11T13:30:38Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-04-11T13:30:38Z"]},{"key":"dc:date.issued","label":"Date","values":["2009"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:type","label":"Dc Type","values":["Thesis / Dissertation"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Applied Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/39363"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["On one class of extensions of Lie algebras and the Casimir functions related to it"]}]}],"canonical_facts":{"dc:contributor.advisor":["lanovsky, Alexandar"],"dc:creator":["dos Santos, Moses Caires"],"dc:date.accessioned":["2024-04-11T13:30:38Z"],"dc:date.available":["2024-04-11T13:30:38Z"],"dc:date.issued":["2009"],"dc:description.abstract":["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."],"dc:identifier.uri":["http://hdl.handle.net/11427/39363"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:subject":["Applied Mathematics"],"dc:title":["On one class of extensions of Lie algebras and the Casimir functions related to it"],"dc:type":["Thesis / Dissertation"],"dc:type.qualificationlevel":["Masters"]},"updated_at":"2026-07-24T01:34:16Z"}