Regular Hom-Lie structures on incidence algebras

TL;DR

This paper characterizes all regular Hom-Lie structures on incidence algebras of finite connected posets, revealing their composition from central maps and automorphisms, thus deepening understanding of algebraic symmetries.

Contribution

It provides a complete description of regular Hom-Lie structures on incidence algebras, combining central maps and automorphisms, a novel characterization in this context.

Findings

Regular Hom-Lie structures are sums of central maps and automorphisms.

Such structures annihilate the Jacobson radical of the algebra.

The characterization applies to incidence algebras of finite connected posets.

Abstract

We fully characterize regular Hom-Lie structures on the incidence algebra $I(X,K)$ of a finite connected poset $X$ over a field $K$. We prove that such a structure is the sum of a central-valued linear map annihilating the Jacobson radical of $I(X,K)$ with the composition of certain inner and multiplicative automorphisms of $I(X,K)$.