Representations of modular skew group algebras

Li, Liping

doi:10.1090/S0002-9947-2015-06242-4

Representations of modular skew group algebras
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Trans. Amer. Math. Soc. 367 (2015), 6293-6314 Request permission

Abstract:

In this paper we study representations of skew group algebras $\Lambda G$, where $\Lambda$ 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 $\Lambda$. 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 $\Lambda$ is a locally finite graded algebra and the action of $G$ on $\Lambda$ preserves grading, we show that $\Lambda G$ is a generalized Koszul algebra if and only if $\Lambda$ is.

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