Jordan $*$-derivations of incidence algebras

Abstract

Let $X$ be a locally finite partially ordered set (poset), $K$ a field of characteristic not 2, and $I(X,K)$ the incidence algebra over $K$. In this paper, we prove that every Jordan $*$-derivation of $I(X,K)$ is an inner $*$-derivation and a transposed Jordan $*$-derivation. Moreover, we demonstrate the existence of Jordan $*$-derivations that are not $*$-derivations.