Noetherian Hopf algebra domains of Gelfand-Kirillov dimension two

被引：31
|
作者：
Goodearl, K. R. [1 ]
Zhang, J. J. [2 ]
机构：
[1] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA
[2] Univ Washington, Dept Math, Seattle, WA 98195 USA
来源：
JOURNAL OF ALGEBRA | 2010年 / 324卷 / 11期
基金：
美国国家科学基金会;
关键词：
Hopf algebra; Noetherian; Gelfand-Kirillov dimension; QUANTUM GROUPS;
D O I：
10.1016/j.jalgebra.2009.11.001
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We classify all noetherian Hopf algebras H over an algebraically closed field k of characteristic zero which are integral domains of Gelfand-Kirillov dimension two and satisfy the condition Ext(H)(1)(k,k) not equal 0. The latter condition is conjecturally redundant, as no examples are known (among noetherian Hopf algebra domains of GK-dimension two) where it fails. (C) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码：3131 / 3168
页数：38
相关论文
共 50 条
  • [11] GELFAND-KIRILLOV DIMENSION
    BORHO, W
    KRAFT, H
    MATHEMATISCHE ANNALEN, 1976, 220 (01) : 1 - 24
  • [12] Simple Z-graded domains of Gelfand-Kirillov dimension two
    Ferraro, Luigi
    Gaddis, Jason
    Won, Robert
    JOURNAL OF ALGEBRA, 2020, 562 : 433 - 465
  • [13] The Gelfand-Kirillov dimension of a weighted Leavitt path algebra
    Preusser, Raimund
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2020, 19 (03)
  • [14] GELFAND-KIRILLOV DIMENSION FOR ALGEBRAS ASSOCIATED WITH WEYL ALGEBRA
    JOSEPH, A
    ANNALES DE L INSTITUT HENRI POINCARE SECTION A PHYSIQUE THEORIQUE, 1972, 17 (04): : 325 - 336
  • [15] Gelfand-Kirillov dimension for rings
    Lezama, Oswaldo
    Venegas, Helbert
    SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, 2020, 14 (01): : 207 - 222
  • [16] SIMPLE ALGEBRAS OF GELFAND-KIRILLOV DIMENSION TWO
    Bell, Jason P.
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 137 (03) : 877 - 883
  • [17] A remark on Gelfand-Kirillov dimension
    Smith, SP
    Zhang, JJ
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (02) : 349 - 352
  • [18] Computing the Gelfand-Kirillov dimension II
    Bueso, JL
    Gómez-Torrecillas, J
    Lobillo, FJ
    RING THEORY AND ALGEBRAIC GEOMETRY, 2001, 221 : 33 - 57
  • [19] Properties of pointed and connected Hopf algebras of finite Gelfand-Kirillov dimension
    Zhuang, Guangbin
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2013, 87 : 877 - 898
  • [20] ON ALGEBRAS WITH GELFAND-KIRILLOV DIMENSION ONE
    KOBAYASHI, S
    KOBAYASHI, Y
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 119 (04) : 1095 - 1104
12345