Lie Derivations of Incidence Algebras

TL;DR

This paper proves that all Lie derivations of incidence algebras over a 2-torsion free ring are proper, enhancing understanding of their algebraic structure.

Contribution

It establishes that every Lie derivation of incidence algebras over 2-torsion free rings is proper, a significant extension in the theory of algebra derivations.

Findings

All Lie derivations are proper under the given conditions

The result applies to incidence algebras over 2-torsion free rings

Advances the understanding of algebraic derivations in incidence algebras

Abstract

Let $X$ be a locally finite preordered set, $\mathcal R$ a commutative ring with identity and $I(X,\mathcal R)$ the incidence algebra of $X$ over $\mathcal R$. In this note we prove that each Lie derivation of $I(X,\mathcal R)$ is proper, provided that $\mathcal R$ is $2$-torsion free.