Hopf bimodules are modules over a diagonal crossed product algebra

被引：6
|
作者：
Panaite, F [1 ]
机构：
[1] Romanian Acad, Inst Math, RO-70700 Bucharest, Romania
来源：
COMMUNICATIONS IN ALGEBRA | 2002年 / 30卷 / 08期
关键词：
D O I：
10.1081/AGB-120005835
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
If H is a finite dimensional Hopf algebra, C. Cibils and M. Rosso found an algebra X having the property that Hopf bimodules over H* coincide with left X-modules. We find two other algebras, Y and Z, having the same property; namely, Y is-the two-sided crossed product H*#(Hcircle timesH(op))#H*(op) and Z is the diagonal crossed product (H*circle timesH*(op)) >< (Hcircle timesH(op)) (both concepts are. due to F. Hausser and F. Nill). We also find explicit isomorphisms between the algebras X, Y, Z.
引用
收藏
页码：4049 / 4058
页数：10
相关论文
共 50 条
  • [1] Diagonal crossed product of multiplier Hopf algebras
    Yan, Dongdong
    Wang, Shuanhong
    [J]. Journal of Southeast University (English Edition), 2020, 36 (02) : 241 - 244
  • [2] Hopf bimodules are modules
    Cibils, C
    Rosso, M
    [J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 1998, 128 (03) : 225 - 231
  • [3] Tensor product of Hopf bimodules over a group
    Cibils, C
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 125 (05) : 1315 - 1321
  • [4] The crossed structure of Hopf bimodules
    Zhu, Haixing
    [J]. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2018, 17 (09)
  • [5] The Crossed Product of Finite Hopf C*-Algebra and C*-Algebra
    Wei, Xiaomin
    Jiang, Lining
    Tian, Dianlu
    [J]. MATHEMATICS, 2021, 9 (09)
  • [6] Invariants of modules over a Hopf algebra
    Ameur, M
    Benayadi, S
    [J]. COMMUNICATIONS IN ALGEBRA, 1996, 24 (10) : 3155 - 3162
  • [7] Doi-Koppinen Hopf bimodules are modules
    Wang, SH
    [J]. COMMUNICATIONS IN ALGEBRA, 2001, 29 (10) : 4671 - 4682
  • [8] The Hopf algebra of diagonal rectangulations
    Law, Shirley
    Reading, Nathan
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 2012, 119 (03) : 788 - 824
  • [9] CROSSED PRODUCTS OF CROSSED MODULES OF HOPF MONOIDS
    Alonso Alvarez, J. N.
    Fernandez Vilaboa, J. M.
    Gonzalez Rodriguez, R.
    [J]. THEORY AND APPLICATIONS OF CATEGORIES, 2018, 33 : 867 - 897
  • [10] Crossed modules and doi-hopf modules
    S. Caenepeel
    G. Militaru
    Zhu Shenglin
    [J]. Israel Journal of Mathematics, 1997, 100 : 221 - 247
12345