Skew group algebras of path algebras and preprojective algebras

Abstract

We compute explicitly up to Morita-equivalence the skew group algebra of a finite group acting on the path algebra of a quiver and the skew group algebra of a finite group acting on a preprojective algebra. These results generalize previous results of Reiten and Riedtmann for a cyclic group acting on the path algebra of a quiver and of Reiten and Van den Bergh for a finite subgroup of $\SL(\C X \oplus \C Y)$ acting on $\C[X, Y]$.