Uma construção alternativa para o funtor de Happel

• Ano de defesa: 2018
• Autor(a) principal: Lima, Maria Elismara de Sousa
• Orientador(a): Silva, Danilo Dias da
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Programa de Pós-Graduação: Pós-Graduação em Matemática
• Palavras-chave em Português: Matemática; Álgebra; Álgebra homológica; Categorias (Matemática); Localização de categorias; Categorias trianguladas; Categoria derivada
• Palavras-chave em Inglês: Localization of categories; Triangulated categories; Derived category
• Link de acesso: http://ri.ufs.br/jspui/handle/riufs/7782

The aim of this dissertation is to present a simpli cation of the proof of the following result obtained rst by Happel in [3]: If A is a nite-dimensional algebra over a eld algebraically closed K, then there is a triangulated, full and faithful functor of triangulated categories H : Db(modA) ! modA^, where A^ is the repetitive algebra obtained from A, which is also dense if A is of nite global dimension. We begin with a succinct presentation of the categorical language, approaching in general terms on the localization of categories, triangulated categories and their localizations, and nally derived categories, which are localized and triangulated categories. We also introduce the stable category of modules of a repetitive algebra A^. In the last chapter, we demonstrate the main result with the help of a result found in [8], in addition to the previously mentioned concepts.