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http://hdl.handle.net/1942/25852
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 | Document URI: | http://hdl.handle.net/1942/25852 | 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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SciSinMath-2018-0471.pdf Restricted Access | Published version | 683.66 kB | Adobe PDF | View/Open Request a copy |
Green-rings-of-spherical-Hopf-algebras(5).pdf Restricted Access | Peer-reviewed author version | 356.1 kB | Adobe PDF | View/Open Request a copy |
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