Connected Hopf algebras and iterated Ore extensions

被引：23

作者：

Brown, K. A. ^{[1
]}

O'Hagan, S. ^{[1
]}

Zhang, J. J. ^{[2
]}

Zhuang, G. ^{[3
]}

机构：

[1] Univ Glasgow, Sch Math & Stat, Glasgow G12 8QW, Lanark, Scotland

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

[3] Univ So Calif, Dept Math, Los Angeles, CA 90089 USA

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2015年 / 219卷 / 06期

基金：

美国国家科学基金会;

关键词：

GELFAND-KIRILLOV DIMENSION; SKEW POLYNOMIAL-RINGS; IDENTITY;

D O I：

10.1016/j.jpaa.2014.09.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate when a skew polynomial extension T = R[x; sigma, delta] of a Hopf algebra R admits a Hopf algebra structure, substantially generalising a theorem of Panov. When this construction is applied iteratively in characteristic 0 one obtains a large family of connected noetherian Hopf algebras of finite Gelfand-Kirillov dimension, including for example all enveloping algebras of finite dimensional solvable Lie algebras and all coordinate rings of unipotent groups. The properties of these Hopf algebras are investigated. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：2405 / 2433

页数：29

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