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Skew categories, smash product categories and quasi-Koszul categories


Author: Deke Zhao
Journal: Proc. Amer. Math. Soc. 139 (2011), 2657-2662
MSC (2010): Primary 18A25, 18G10; Secondary 18B99
DOI: https://doi.org/10.1090/S0002-9939-2011-10695-6
Published electronically: January 11, 2011
MathSciNet review: 2801604
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Abstract: Let $ \mathscr{A}$ be a small additive Krull-Schmidt locally radical finite category over a field $ K$ and let $ G$ be a finite group. We show that if $ \mathscr{A}$ is a free $ G$-category (resp. $ G$-graded category), then $ \mathscr{A}$ is quasi-Koszul if and only if the skew (resp. smash product) category $ G*\mathscr{A}$ (resp. $ \mathscr{A}\char93 G$) is.


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Additional Information

Deke Zhao
Affiliation: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
Address at time of publication: School of Applied Mathematics, Beijing Normal University at Zhuhai, Zhuhai, 519087, People’s Republic of China
Email: deke@amss.ac.cn

DOI: https://doi.org/10.1090/S0002-9939-2011-10695-6
Keywords: Skew categories, smash product categories, quasi-Koszul categories, group-graded categories.
Received by editor(s): November 22, 2009
Received by editor(s) in revised form: July 12, 2010
Published electronically: January 11, 2011
Communicated by: Martin Lorenz
Article copyright: © Copyright 2011 American Mathematical Society

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