Lie automorphisms of incidence algebras

TL;DR

This paper characterizes the Lie automorphisms of incidence algebras over finite connected posets, revealing that most are not proper automorphisms, thus deepening understanding of their algebraic structure.

Contribution

It provides a complete description of Lie automorphisms of incidence algebras, highlighting that they are generally not proper automorphisms, which was previously unclear.

Findings

Lie automorphisms are fully characterized

Most Lie automorphisms are not proper automorphisms

Enhances understanding of incidence algebra symmetries

Abstract

Let $X$ be a finite connected poset and $K$ a field. We give a full description of the Lie automorphisms of the incidence algebra $I(X,K)$. In particular, we show that they are in general not proper.