O anel de GREEN da álgebra de TAFT

• Ano de defesa: 2019
• Autor(a) principal: Pedrotti, Juliana Borges
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Santa Maria; Brasil; Matemática; UFSM; Programa de Pós-Graduação em Matemática; Centro de Ciências Naturais e Exatas
• Palavras-chave em Português: Álgebra de Taft; Anel de Green; Módulos indecomponíveis; Produto tensorial de módulos; Taft algebra; Green ring; Indecomposable modules; Tensor product of modules; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://repositorio.ufsm.br/handle/1/19351

The aim of this work is to characterize the Green ring of Taft algebra, denoted by ��(�), where � is a positive integer greater than 1 and � is a primitive root of unity of order �. The Green ring, denoted by �(��(�)), is generated by the isomorphism classes [�] of finite dimensional ��(�)-modules with addition given by [�] + [�] = [� ⊕ �] and multiplication given by the tensor product and it has a -basis given by the classes of isomorphisms of indecomposable finite dimensional ��(�)-modules. In this work we describe the indecomposable ��(�)-modules and the tensorial product between these. From that we show that �(��(�)) is a commutative ring generated by two elements subject to certain relations.