Polynomial identities with involution for the algebra of 3 × 3 upper triangular matrices

2020/07/08 by Dimas José Gonçalves, Gonçalves, Dimas J., Dalton C. Silva +1
Mathematics · #16R10 #16R50 #16W10 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2007.04112

openalex publication_date 2020/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathbbF be a field of characteristic p, and let UT_n(\mathbbF) be the algebra of n × n upper triangular matrices over \mathbbF with an involution of the first kind. In this paper we describe: the set of all *-central polynomials for UT_n(\mathbbF) when n≥ 3 and p≠ 2 ; the set of all *-polynomial identities for UT₃(\mathbbF) when \mathbbF is infinite and p>2.

Citations

• Finite basis problem for identities with involution

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