Identidades polinomiais para a álgebra de Jordan das matrizes triangulares superiores 2x2 - Salomão, Mateus Eduardo (Universidade Federal de São Carlos, 2021)
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.
Polynomial identities for the Jordan algebra of 2x2 upper triangular matrices
Keywords: 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