Skew group algebras of path algebras and preprojective algebras

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 (1985) [RR], for a cyclic group acting on the path algebra of a quiver and of Reiten and Van den Bergh (1989) [RV, Proposition 2.13] for a finite subgroup of SL(CX⊕CY) acting on C[X,Y].