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arXiv · 2007.04112

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

Dimas J. Gonçalves·Dalton C. Silva
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Abstract

Let $\mathbb{F}$ be a field of characteristic $p$, and let $UT_n(\mathbb{F})$ 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 $*$-central polynomials for $UT_n(\mathbb{F})$ when $n\geq 3$ and $p\neq 2$ ; the set of all $*$-polynomial identities for $UT_3(\mathbb{F})$ when $\mathbb{F}$ is infinite and $p>2$.

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BibTeXRIS

Dimas J. Gonçalves, Dalton C. Silva. 2020-07-08. Polynomial identities with involution for the algebra of 3 $\times$ 3 upper triangular matrices. https://arxiv.org/abs/2007.04112

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