Lie Derivations of Dual Extension Algebras

Abstract

Let $K$ be a field and $\Gamma$ a finite quiver without oriented cycles. Let $\Lambda$ be the path algebra $K(\Gamma ,\rho )$ and let $\mathcal{D}(\Lambda )$ be the dual extension of $\Lambda$. In this paper, we prove that each Lie derivation of $\mathcal{D}(\Lambda )$ is of the standard form.

16 pages