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

Abstract

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.