Representations of Modular Skew Group Algebras

Abstract

In this paper we study representations of skew group algebras $ΛG$, where $Λ$ is a connected, basic, finite-dimensional algebra (or a locally finite graded algebra) over an algebraically closed field $k$ with characteristic $p \geqslant 0$, and $G$ is an arbitrary finite group each element of which acts as an algebra automorphism on $Λ$. We characterize skew group algebras with finite global dimension or finite representation type, and classify the representation types of transporter categories for $p \neq 2,3$. When $Λ$ is a locally finite graded algebra and the action of $G$ on $Λ$ preserves grading, we show that $ΛG$ is a generalized Koszul algebra if and only if so is $Λ$.