Lie Derivations of Dual Extension Algebras

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