The Green rings of Taft algebras

Chen, Huixiang; Van Oystaeyen, Fred; Zhang, Yinhuo

doi:10.1090/S0002-9939-2013-11823-X

The Green rings of Taft algebras
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by Huixiang Chen, Fred Van Oystaeyen and Yinhuo Zhang

Proc. Amer. Math. Soc. 142 (2014), 765-775

DOI: https://doi.org/10.1090/S0002-9939-2013-11823-X

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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