POINTED HOPF ALGEBRAS WITH CLASSICAL WEYL GROUPS

被引：3
|
作者：
Zhang, Shouchuan [1 ]
Zhang, Yao-Zhong [2 ]
机构：
[1] Hunan Univ, Dept Math, Changsha 410082, Hunan, Peoples R China
[2] Univ Queensland, Sch Math & Phys, Brisbane, Qld 4072, Australia
来源：
INTERNATIONAL JOURNAL OF MATHEMATICS | 2012年 / 23卷 / 06期
基金：
澳大利亚研究理事会;
关键词：
Quiver; Hopf algebra; Weyl group;
D O I：
10.1142/S0129167X12500668
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that Nichols algebras of irreducible Yetter-Drinfeld modules over classical Weyl groups A (sic) S-n supported by S-n are infinite dimensional, except in three cases. We give necessary and sufficient conditions for Nichols algebras of Yetter-Drinfeld modules over classical Weyl groups A (sic) S-n supported by A to be finite dimensional.
引用
收藏
页数：26
相关论文
共 50 条
  • [31] Baxter algebras and Hopf algebras
    Andrews, GE
    Guo, L
    Keigher, W
    Ono, K
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 355 (11) : 4639 - 4656
  • [32] Centrification of algebras and Hopf algebras
    Rumynin, Dmitriy
    Westaway, Matthew
    CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2022, 65 (01): : 155 - 169
  • [33] Lattice structure of Weyl groups via representation theory of preprojective algebras
    Iyama, Osamu
    Reading, Nathan
    Reiten, Idun
    Thomas, Hugh
    COMPOSITIO MATHEMATICA, 2018, 154 (06) : 1269 - 1305
  • [34] ON HOPF ALGEBRAS OVER BASIC HOPF ALGEBRAS OF DIMENSION 24
    Xiong, Rongchuan
    REVISTA DE LA UNION MATEMATICA ARGENTINA, 2023, 65 (02): : 469 - 493
  • [35] Braided Hopf Algebras Obtained from Coquasitriangular Hopf Algebras
    Margaret Beattie
    Daniel Bulacu
    Communications in Mathematical Physics, 2008, 282 : 115 - 160
  • [36] A note on the order of the antipode of a pointed Hopf algebra
    Gilmartin, Paul
    COMMUNICATIONS IN ALGEBRA, 2019, 47 (07) : 2833 - 2842
  • [37] Weyl groups of fine gradings on matrix algebras, octonions and the Albert algebra
    Elduque, Alberto
    Kochetov, Mikhail
    JOURNAL OF ALGEBRA, 2012, 366 : 165 - 186
  • [38] Representations of a non-pointed Hopf algebra
    Yang, Ruifang
    Yang, Shilin
    AIMS MATHEMATICS, 2021, 6 (10): : 10523 - 10539
  • [39] Classification of PM quiver Hopf algebras
    Zhang, Shouchuan
    Zhang, Yao-Zhong
    Chen, Hui-Xiang
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2007, 6 (06) : 919 - 950
  • [40] Generalized Frobenius Algebras and Hopf Algebras
    Iovanov, Miodrag Cristian
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2014, 66 (01): : 205 - 240
12345