Polynomial identities for the Jordan algebra of 2 x 2 upper triangular matrices

Author(s)

Goncalves, Dimas Jose ; Koshlukov, Plamen ; Salomao, Mateus Eduardo

• Document type: Journal article
• Source: Journal of Algebra; v. 593, p. 30-pg., 2022-03-01.

Abstract

Let K be a field (finite or infinite) of char(K) &NOTEQUexpressionL; 2 and let UT2(K) be the 2 x 2 upper triangular matrix algebra over K. If center dot is the usual product on UT2(K) then with the new product a b = (1/2)(a center dot b + b center dot a) we have that UT2(K) is a Jordan algebra, denoted by UJ(2) = UJ(2)(K). In this paper, we describe the set I of all polynomial identities of UJ(2) and a linear basis for the corresponding relatively free algebra. Moreover, if K is infinite we prove that I has the Specht property. In other words I, and every T-ideal containing I, is finitely generated as a T-ideal. (C) 2021 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 18/23690-6 - Structures, representations, and applications of algebraic systems
• Grantee: Ivan Chestakov
• Support Opportunities: Research Projects - Thematic Grants