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Title: The Green rings of the generalized Taft algebras
Authors: Li, Libin
ZHANG, Yinhuo 
Issue Date: 2013
Source: Andruskiewitsch, Nicolás; Cuadra, Juan; Torrecillas, Blas (Ed.). Contemporary Mathematics 585 : Hopf Algebras and Tensor Categories, p. 275-288
Series/Report: Contemporary Mathematics
Series/Report no.: 585
Abstract: In this paper, we investigate the Green ring r(Hn,d) of the generalized Taft algebra Hn,d, extending the results of Chen, Van Oystaeyen and Zhang (to appear in Proc. of AMS). We shall determine all nilpotent elements of the Green ring r(Hn,d). It turns out that each nilpotent element in r(Hn,d) can be written as a sum of indecomposable projective representations. The Jacobson radical J(r(Hn,d)) of r(Hn,d) is generated by one element, and its rank is n −n/d. Moreover, we will present all the finite dimensional indecomposable representations over the complexified Green ring R(Hn,d) of Hn,d. Our analysis is based on the decomposition of the tensor product of indecomposable representations and the observation of the solutions for the system of equations associated to the generating relations of the Green ring r(Hn,d).
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ISBN: 978-0-8218-7564-3
DOI: 10.1090/conm/585/11618
Category: C1
Type: Proceedings Paper
Appears in Collections:Research publications

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