Properties of pointed and connected Hopf algebras of finite Gelfand-Kirillov dimension

被引：32

作者：

Zhuang, Guangbin ^{[1
]}

机构：

[1] Univ Washington, Dept Math, Seattle, WA 98195 USA

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2013年 / 87卷

基金：

美国国家科学基金会;

关键词：

SUBALGEBRAS;

D O I：

10.1112/jlms/jds079

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let H be a pointed Hopf algebra. We show that under some mild assumptions H and its associated graded Hopf algebra gr H have the same Gelfand-Kirillov dimension (GK-dimension). As an application, we prove that the GK-dimension of a connected Hopf algebra is either infinity or a positive integer. We also classify connected Hopf algebras of GK-dimension 3 over an algebraically closed field of characteristic 0.

引用

页码：877 / 898

页数：22

共 50 条

[1] CONNECTED HOPF ALGEBRAS OF GELFAND-KIRILLOV DIMENSION FOUR
Wang, D-G
Zhang, J. J.
Zhuang, G.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 367 (08) : 5597 - 5632
[2] GELFAND-KIRILLOV DIMENSION OF COSEMISIMPLE HOPF ALGEBRAS
Chirvasitu, Alexandru
Walton, Chelsea
Wang, Xingting
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 147 (11) : 4665 - 4672
[3] Lie algebras with finite Gelfand-Kirillov dimension
Riley, D
Usefi, H
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 133 (06) : 1569 - 1572
[4] LEAVITT PATH ALGEBRAS OF FINITE GELFAND-KIRILLOV DIMENSION
Alahmadi, Adel
Alsulami, Hamed
Jain, S. K.
Zelmanov, Efim
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2012, 11 (06)
[5] *-Orderings and *-valuations on algebras of finite Gelfand-Kirillov dimension
Marshall, M
JOURNAL OF PURE AND APPLIED ALGEBRA, 2003, 179 (03) : 255 - 271
[6] The Dixmier-Moeglin Equivalence for Cocommutative Hopf Algebras of Finite Gelfand-Kirillov Dimension
Jason P. Bell
Wing Hong Leung
Algebras and Representation Theory, 2014, 17 : 1843 - 1852
[7] The Dixmier-Moeglin Equivalence for Cocommutative Hopf Algebras of Finite Gelfand-Kirillov Dimension
Bell, Jason P.
Leung, Wing Hong
ALGEBRAS AND REPRESENTATION THEORY, 2014, 17 (06) : 1843 - 1852
[8] ON ALGEBRAS WITH GELFAND-KIRILLOV DIMENSION ONE
KOBAYASHI, S
KOBAYASHI, Y
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 119 (04) : 1095 - 1104
[9] Graph algebras and the Gelfand-Kirillov dimension
Moreno-Fernandez, Jose M.
Siles Molina, Mercedes
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2018, 17 (05)
[10] GELFAND-KIRILLOV DIMENSION OF PI ALGEBRAS
MALLIAVINBRAMERET, MP
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1976, 282 (13): : 679 - 681

← 1 2 3 4 5 →