Representations of a non-pointed Hopf algebra

被引：2
|
作者：
Yang, Ruifang [1 ]
Yang, Shilin [1 ]
机构：
[1] Beijing Univ Technol, Fac Sci, Coll Math, Beijing 100124, Peoples R China
来源：
AIMS MATHEMATICS | 2021年 / 6卷 / 10期
基金：
中国国家自然科学基金;
关键词：
Hopf algebra; representation type; indecomposable module; tensor product; representation ring; GREEN RINGS;
D O I：
10.3934/math.2021611
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we construct all the indecomposable modules of a class of non-pointed Hopf algebras, which are quotient Hopf algebras of a class of prime Hopf algebras of GK-dimension one. Then the decomposition formulas of the tensor product of any two indecomposable modules are established. Based on these results, the representation ring of the Hopf algebras is characterized by generators and some relations.
引用
收藏
页码：10523 / 10539
页数：17
相关论文
共 50 条
  • [31] ANTIPODES IN POINTED HOPF ALGEBRAS
    TAFT, EJ
    WILSON, RL
    [J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 19 (07): : A785 - A785
  • [32] Duals of pointed Hopf algebras
    Beattie, M
    [J]. JOURNAL OF ALGEBRA, 2003, 262 (01) : 54 - 76
  • [33] Forms of pointed Hopf algebras
    Caenepeel, S
    Dascalescu, S
    Le Bruyn, L
    [J]. MANUSCRIPTA MATHEMATICA, 1999, 100 (01) : 35 - 53
  • [34] The Lasker-Noether theorem for commutative and noetherian module algebras over a pointed Hopf algebra
    Tyc, A
    Wisniewski, P
    [J]. JOURNAL OF ALGEBRA, 2003, 267 (01) : 58 - 95
  • [35] ANTIPODES IN POINTED HOPF ALGEBRAS
    TAFT, EJ
    WILSON, RL
    [J]. JOURNAL OF ALGEBRA, 1974, 29 (01) : 27 - 32
  • [36] Forms of pointed Hopf algebras
    S. Caenepeel
    S. Dăscălescu
    L. Le Bruyn
    [J]. manuscripta mathematica, 1999, 100 : 35 - 53
  • [37] On pointed ribbon Hopf algebras
    Gelaki, S
    [J]. JOURNAL OF ALGEBRA, 1996, 181 (03) : 760 - 786
  • [38] POINTED HOPF ALGEBRAS ARE FREE OVER HOPF SUBALGEBRAS
    RADFORD, DE
    [J]. JOURNAL OF ALGEBRA, 1977, 45 (02) : 266 - 273
  • [39] POINTED HOPF ACTIONS ON FIELDS, I
    PAVEL ETINGOF
    CHELSEA WALTON
    [J]. Transformation Groups, 2015, 20 : 985 - 1013
  • [40] Pointed Hopf actions on fields, II
    Etingof, Pavel
    Walton, Chelsea
    [J]. JOURNAL OF ALGEBRA, 2016, 460 : 253 - 283
12345