Skew group algebras of path algebras and preprojective algebras

TL;DR

This paper explicitly computes skew group algebras for finite groups acting on path and preprojective algebras, generalizing earlier results for cyclic groups and specific subgroup actions.

Contribution

It provides explicit Morita-equivalence classifications of skew group algebras for broader classes of group actions on these algebras, extending previous work.

Findings

Explicit Morita-equivalence classifications

Generalization of cyclic group results

Extension to broader group actions

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 $\C[X, Y]$.