Connected Hopf algebras and iterated Ore extensions

Brown, K.A. , O'Hagan, S., Zhang, J.J. and Zhuang, G. (2015) Connected Hopf algebras and iterated Ore extensions. Journal of Pure and Applied Algebra, 219, pp. 2405-2443. (doi:10.1016/j.jpaa.2014.09.007)

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Abstract

We investigate when a skew polynomial extension T=R[x;σ,δ] 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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:O'Hagan, Mr Steven and Brown, Professor Ken
Authors: Brown, K.A., O'Hagan, S., Zhang, J.J., and Zhuang, G.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Pure and Applied Algebra
Journal Abbr.:J. Pure App. Algbera
Publisher:Elsevier B.V.
ISSN:0022-4049
ISSN (Online):1873-1376
First Published:First Published in Journal of Pure and Applied Algebra 219:2405-2443
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