The Green rings of Taft algebras

We compute the Green ring of the Taft algebra Hn(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(Hn(q)) of the Taft algebra Hn(q) is a commutative ring generated by two elements subject to certain relations defined recursively. Conc...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2014-03, Vol.142 (3), p.765-775
Main Authors: CHEN, HUIXIANG, VAN OYSTAEYEN, FRED, ZHANG, YINHUO
Format: Article
Language:English
Subjects:
Algebra
Commutativity
Integers
Linear algebra
Mathematical induction
Mathematical rings
Mathematical theorems
Polynomials
Quotients
Tensors
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Summary:We compute the Green ring of the Taft algebra Hn(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(Hn(q)) of the Taft algebra Hn(q) is a commutative ring generated by two elements subject to certain relations defined recursively. Concrete examples for n = 2, 3,..., 8 are given.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-2013-11823-X