Uma resolução livre para certas álgebras

• Ano de defesa: 2020
• Autor(a) principal: Araujo Junior, Hilario Fernandes De [UNIFESP]
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de São Paulo (UNIFESP)
• Palavras-chave em Português: Free Resolution; Homological Algebra; Kac-Moody Algebras; Shirshov-Gröbner Bases; Álgebra Homológica; Álgebras De Kac-Moody; Bases De Shirshov-Gröbner; Resolução Livre
• Link de acesso: https://sucupira.capes.gov.br/sucupira/public/consultas/coleta/trabalhoConclusao/viewTrabalhoConclusao.jsf?popup=true&id_trabalho=10026736; https://hdl.handle.net/11600/64910

The notion of resolutions in homological algebra is generally used to define invariants that characterize an algebraic structure. The objective of this dissertation is to study a free resolution for associative algebras by David Anick. This free resolution is adequate to determine the homology of an algebra, that is the calculation of the Tor functor and the Poincaré series. We specialize Anick’s result in the context of the universal enveloping algebras for certain Lie algebras, with the support of Shirshov-Gröbner bases theory.