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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Green rings of Taft algebras


Authors: Huixiang Chen, Fred Van Oystaeyen and Yinhuo Zhang
Journal: Proc. Amer. Math. Soc. 142 (2014), 765-775
MSC (2010): Primary 16G10, 16T05
Published electronically: November 26, 2013
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Abstract: We compute the Green ring of the Taft algebra $ H_n(q)$, where $ n$ is a positive integer greater than 1 and $ q$ is an $ n$-th root of unity. It turns out that the Green ring $ r(H_n(q))$ of the Taft algebra $ H_n(q)$ is a commutative ring generated by two elements subject to certain relations defined recursively. Concrete examples for $ n=2,3, ... , 8$ are given.


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Additional Information

Huixiang Chen
Affiliation: School of Mathematical Science, Yangzhou University, Yangzhou 225002, People’s Republic of China
Email: hxchen@yzu.edu.cn

Fred Van Oystaeyen
Affiliation: Department of Mathematics and Computer Science, University of Antwerp, Middelheimlaan 1, B-2020 Antwerp, Belgium
Email: fred.vanoystaeyen@ua.ac.be

Yinhuo Zhang
Affiliation: Department WNI, University of Hasselt, Universitaire Campus, 3590 Diepeenbeek, Belgium
Email: yinhuo.zhang@uhasselt.be

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11823-X
PII: S 0002-9939(2013)11823-X
Keywords: Green ring, indecomposable module, Taft algebra
Received by editor(s): November 9, 2011
Received by editor(s) in revised form: March 9, 2012, and April 5, 2012
Published electronically: November 26, 2013
Additional Notes: The first-named author would like to thank the Department of Mathematics, University of Antwerp, for its hospitality during his visit in 2011. He is grateful to the Belgium FWO for financial support. He was also supported by NSF of China (No. 11171291).
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2013 American Mathematical Society