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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/17952

Title: Green Rings of Pointed Rank One Hopf Algebras of Nilpotent Type
Authors: WANG, Zhihua
Li, Libin
ZHANG, Yinhuo
Issue Date: 2014
Citation: ALGEBRAS AND REPRESENTATION THEORY, 17 (6), p. 1901-1924
Abstract: Let H be a finite dimensional pointed rank one Hopf algebra of nilpotent type. We first determine all finite dimensional indecomposable H-modules up to isomorphism, and then establish the Clebsch-Gordan formulas for the decompositions of the tensor products of indecomposable H-modules by virtue of almost split sequences. The Green ring r(H) of H will be presented in terms of generators and relations. It turns out that the Green ring r(H) is commutative and is generated by one variable over the Grothendieck ring G0(H) of H modulo one relation. Moreover, r(H) is Frobenius and symmetric with dual bases associated to almost split sequences, and its Jacobson radical is a principal ideal. Finally, we show that the stable Green ring, the Green ring of the stable module category, is isomorphic to the quotient ring of r(H) modulo all projective modules. It turns out that the complexified stable Green algebra is a group-like algebra and hence a bi-Frobenius algebra.
Notes: Z. Wang; Y. Zhang: Department of Mathematics and Statistics, University of Hasselt, 3590 Diepeenbeek, Belgium e-mail: yinhuo.zhang@uhasselt.be Z. Wang: e-mail: mailzhihua@gmail.com Z. Wang; L. Li: School of Mathematical Science, Yangzhou University, Yangzhou 225002, China L. Li: e-mail: lbli@yzu.edu.cn
URI: http://hdl.handle.net/1942/17952
Link to publication: http://link.springer.com/article/10.1007%2Fs10468-014-9484-9#page-1
DOI: 10.1007/s10468-014-9484-9
ISI #: 000345967200015
ISSN: 1386-923X
Category: A1
Type: Journal Contribution
Validation: ecoom, 2016
Appears in Collections: Research publications

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