Regular Hom-Lie structures on incidence algebras

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).