# Lie Triple Derivations of Incidence Algebras

## TL;DR

This paper proves that all Lie triple derivations of incidence algebras over certain rings are proper when the underlying pre-ordered set has finitely many connected components.

## Contribution

It establishes a condition under which Lie triple derivations of incidence algebras are necessarily proper, extending understanding of their algebraic structure.

## Key findings

- Lie triple derivations are proper for incidence algebras over finite connected components
- The result applies to 2-torsion free commutative rings with unity
- Provides a characterization of derivations in this algebraic context

## Abstract

Let $\mathcal{R}$ be a $2$-torsion free commutative ring with unity, $X$ a locally finite pre-ordered set and $I(X,\mathcal{R})$ the incidence algebra of $X$ over $\mathcal{R}$. If $X$ consists of a finite number of connected components, we prove in this paper that every Lie triple derivation of $I(X,\mathcal{R})$ is proper.