Central polynomials with involution for the algebra of $2\times 2$ upper triangular matrices

Abstract

Let F be a field of characteristic different from $2$, and let $U{T}_2(F)$ be the algebra of $2\times 2$ upper triangular matrices over $F$. For every involution of the first kind on $U{T}_2(F)$, we describe the set of all $\ast$-central polynomials for this algebra.