Identidades polinomiais para a álgebra de Jordan das matrizes triangulares superiores 2x2

• Autor(a) principal: Salomão, Mateus Eduardo
• Data de Publicação: 2021
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da UFSCAR
• Texto Completo: https://repositorio.ufscar.br/handle/ufscar/15149
• topic: Ágebra das matrizes triangulares superiores; Álgebra de Jordan; Identidades polinomiais; Álgebra graduada; Identidades polinomiais graduadas; Propriedade de Specht; Upper triangular matrix algebra; Jordan algebra; Polynomial identities; Graded algebra; Graded polynomial identities; Specht property; CIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRA

Let K be a field (finite or infinite) of char(K) ≠ 2, and let UTn = UTn(K) be the n x n upper triangular matrix algebra over K. If · is the usual product on UTn, then with the new product a ○ b = (1/2)(a·b + b·a), UTn becomes a Jordan algebra, denoted by UJn = UJn(K). In this thesis, we describe the set I of all polynomial identities of UJ2 for any K, and we prove that I has the Specht property when K is infinite, namely that, I and every T-ideal containing I, is finitely generated as a T-ideal. Moreover, we describe the set of all Z2-graded polynomial identities of UJ2 with any Z2-grading, and we describe a linear basis for the corresponding relatively free Z2-graded algebra.