Images of multilinear graded polynomials on upper triangular matrix algebras

Author(s)

Fagundes, Pedro ; Koshlukov, Plamen

• Document type: Journal article
• Source: CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES; v. N/A, p. 26-pg., 2022-09-19.

Abstract

In this paper, we study the images of multilinear graded polynomials on the graded algebra of upper triangular matrices UTn. For positive integers q <= n, we classify these images on UTn endowed with a particular elementary Z(q)-grading. As a consequence, we obtain the images of multilinear graded polynomials on UTn with the natural Z(n)-grading. We apply this classification in order to give a new condition for a multilinear polynomial in terms of graded identities so that to obtain the traceless matrices in its image on the full matrix algebra. We also describe the images of multilinear polynomials on the graded algebras UT2 and UT3, for arbitrary gradings. We finish the paper by proving a similar result for the graded Jordan algebra UJ(2), and also for UJ(3) endowed with the natural elementary Z(3)-grading. (AU)

• FAPESP's process: 18/23690-6 - Structures, representations, and applications of algebraic systems
• Grantee: Ivan Chestakov
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 19/16994-1 - Algebras that are sums of two PI subalgebras
• Grantee: Pedro Souza Fagundes
• Support Opportunities: Scholarships in Brazil - Doctorate