Teoremas de Maschke

• Ano de defesa: 2013
• Autor(a) principal: Santos, Ricardo Leite dos
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• dARK ID: ark:/26339/001300000w28k
• Idioma: por
• Instituição de defesa: Universidade Federal de Santa Maria; BR; Matemática; UFSM; Programa de Pós-Graduação em Matemática
• Palavras-chave em Português: Teoremas de Maschke; Semissimples; Ações parciais de grupos; Produto cruzado; Álgebras de Hopf; Semisimple; Partial actions of groups; Crossed product; Hopf algebra; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://repositorio.ufsm.br/handle/1/9981

In representation theory, having a representation of a group G is equivalent to having a kG-module. Since |G-modules which are sums of irreducible kG-modules form a very important class in the theory of modules, to know conditions for a kG-module be irreducible or completely reducible from the particularities of the field k and the group G become a very important issue, whose solution was originally presented by the German mathematician Heinrich Maschke which proved that if the order of G is not a multiple of the characteristic of the field k, then kG is completely reducible (or semisimple). From there, issues unrelated to representation theory, but that concern the semisimplicity of cross products in general are treated as Maschke-type theorem. Our goal in this dissertation is to present some versions of this theorem, starting with classic versions involving cross products for actions of groups on algebras and then versions for Hopf algebras and smash products.