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Title: Construct bi-frobenius algebras via the Benson-Carlson quotient rings
Authors: Wang, Zhihua
Li, Libin
ZHANG, Yinhuo 
Issue Date: 2018
Source: SCIENTIA SINICA Mathematica, 48(4), p. 471-482
Abstract: Let H be a finite dimensional spherical Hopf algebra, r(H) the Green ring of H and P the ideal of r(H) generated by all H-modules of quantum dimension zero. Using dimensions of negligible morphism spaces, we define a bilinear form on the Green ring r(H). This form is associative, symmetric and its radical is annihilator of a certain central element of r(H). After that we consider the Benson-Carlson quotient ring r(H)/P of r(H). This quotient ring can be thought of as the Green ring of a factor category of H-module category. Moreover, if H is of finite representation type, the Benson-Carlson quotient ring admits group-like algebra as well as bi-Frobenius algebra structure.
Keywords: green ring; spherical Hopf algebra; group-like algebra; biFrobenius algebra
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ISSN: 1674-7216
DOI: 10.1360/SCM-2017-0211
Rights: (C) 2017《中国科学》杂志社
Category: A2
Type: Journal Contribution
Appears in Collections:Research publications

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