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Author:

Yang, Ruifang (Yang, Ruifang.) | Yang, Shilin (Yang, Shilin.) (Scholars:杨士林)

Indexed by:

Scopus SCIE

Abstract:

Wu-Liu-Ding algebras, that is D(m, d, xi), are a class of non-pointed affine prime regular Hopf algebras of GK-dimension one. In this paper, we mainly study a class of quotient algebras of D(m, d, xi), denoted by D'(m, d, xi), which are 2m(2)d-dimensional non-pointed semisimple Hopf algebras. For a better understanding of the structure of the Hopf algebra D'(m, d, xi), we have considered the Grothendieck rings of D'(m, d, xi) and their Casimir numbers when d is odd in our previous paper. In this paper we continue dealing with the more complex case when d is even. It turns out that the Grothendieck rings of D'(m, d, xi) are generated by four elements subject to some relations. Then we give the Casimir numbers of the Grothendieck rings of D'(1, d, xi) and D'(2, d, xi).

Keyword:

Frobenius algebra Casimir number Grothendieck ring

Author Community:

  • [ 1 ] [Yang, Ruifang]Beijing Univ Technol, Coll Math, Fac Sci, Beijing, Peoples R China
  • [ 2 ] [Yang, Shilin]Beijing Univ Technol, Coll Math, Fac Sci, Beijing, Peoples R China

Reprint Author's Address:

  • 杨士林

    [Yang, Shilin]Beijing Univ Technol, Coll Math, Fac Sci, Beijing, Peoples R China

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Source :

COMMUNICATIONS IN ALGEBRA

ISSN: 0092-7872

Year: 2020

Issue: 5

Volume: 49

Page: 2041-2073

0 . 7 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

ESI HC Threshold:46

Cited Count:

WoS CC Cited Count: 3

SCOPUS Cited Count: 2

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 1

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