Identidades e polinômios centrais com involução para a álgebra de Grassmann e álgebra das matrizes triangulares de ordem 3

• Autor(a) principal: Silva, Dalton Couto
• Data de Publicação: 2020
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da UFSCAR
• Texto Completo: https://repositorio.ufscar.br/handle/ufscar/13672
• topic: Identidades polinomiais; Polinômios centrais; Álgebra de Grassmann; Matrizes triangulares superiores; Álgebra com involução; Polynomial identities; Central polynomials; Grassmann algebra; Upper triangular matrices; Algebra with Involution; CIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRA::GRUPOS DE ALGEBRA NAO-COMUTAVIVA; CIENCIAS EXATAS E DA TERRA::MATEMATICA; CIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRA

Let F be an infinite field of characteristic different from 2. In this thesis we will study the polynomial identities and central polynomials with involution for two important classes of algebras. More precisely, we describe completely the set of all polynomial identities with involution and the set of all central polynomials with involution for the Grassmann algebra E, when the involution * is arbitrary. Afterwards, we describe the set of all polynomial identities with involution for the algebra of upper triangular matrices of order 3, UT_3(F), when F is an infinite field of characteristic p bigger or equal 3 and the involution is of the first type. Finally, given an arbitrary involution of the first type for UT_n(F), with n bigger or equal 3, we verify that its only central polynomials with involution are the trivial ones.