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

## TL;DR

This paper characterizes all *-central polynomials for the algebra of 2x2 upper triangular matrices over a field with involution of the first kind, expanding understanding of polynomial identities in this algebra.

## Contribution

It provides a complete description of *-central polynomials for UT_2(F) with involution of the first kind, a new result in the theory of polynomial identities.

## Key findings

- Describes all *-central polynomials for UT_2(F) with involution of the first kind.
- Extends the understanding of polynomial identities in upper triangular matrix algebras.
- Contributes to the classification of polynomial identities with involution.

## Abstract

Let F be a field of characteristic different from $2$, and let $UT_2(F)$ be the algebra of $2\times 2$ upper triangular matrices over $F$. For every involution of the first kind on $UT_2(F)$, we describe the set of all $*$-central polynomials for this algebra.