Polynomial identities with involution for the algebra of 3 $\times$ 3 upper triangular matrices

Abstract

Let $\mathbb{F}$ be a field of characteristic $p$, and let $U{T}_n(\mathbb{F})$ be the algebra of $n\times n$ upper triangular matrices over $\mathbb{F}$ with an involution of the first kind. In this paper we describe: the set of all $\ast$-central polynomials for $U{T}_n(\mathbb{F})$ when $n\ge 3$ and $p\ne 2$ ; the set of all $\ast$-polynomial identities for $U{T}_3(\mathbb{F})$ when $\mathbb{F}$ is infinite and $p>2$.

28 pages

References in corpus (1)

• Finite basis problem for identities with involution