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Representations of modular skew group algebras


Author: Liping Li
Journal: Trans. Amer. Math. Soc. 367 (2015), 6293-6314
MSC (2010): Primary 16E10, 16G10, 16G60
DOI: https://doi.org/10.1090/S0002-9947-2015-06242-4
Published electronically: March 13, 2015
MathSciNet review: 3356938
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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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Additional Information

Liping Li
Affiliation: Department of Mathematics, University of California, Riverside, California 92521
Email: lipingli@math.ucr.edu

DOI: https://doi.org/10.1090/S0002-9947-2015-06242-4
Received by editor(s): December 11, 2012
Received by editor(s) in revised form: June 25, 2013
Published electronically: March 13, 2015
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.