Commuting maps of inflated algebras

TL;DR

This paper investigates commuting maps on inflated algebras, showing they are linear up to a scalar and a central-valued linear map, under certain field characteristic conditions.

Contribution

It characterizes the structure of commuting maps on inflated algebras, revealing they are linear plus a central-valued component, which is a novel structural insight.

Findings

Every commuting map on such an algebra has the form $ heta(x)=c x+ u(x)$

The scalar $c$ belongs to the base field $K$ with characteristic not 2

The map $ u$ is a central-valued linear map

Abstract

Commuting maps on a class of algebras called inflated algebras are investigated. In particular, we can prove that every commuting map $\theta$ on such an algebra is of the form $\theta(x)=c x+\mu(x)$, where $c$ belongs to the base field $K$ of characteristic not 2, and $\mu$ is a central-valued linear map.