The finite dual of commutative-by-finite Hopf algebras

Brown, K. A. , Couto, M. and Jahn, A. (2022) The finite dual of commutative-by-finite Hopf algebras. Glasgow Mathematical Journal, (doi: 10.1017/S0017089522000052) (Early Online Publication)

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Abstract

The finite dual H◦ of an affine commutative-by-finite Hopf algebra H is studied. Such a Hopf algebra H is an extension of an affine commutative Hopf algebra A by a finite dimensional Hopf algebra H. The main theorem gives natural conditions under which H◦ decomposes as a crossed or smash product of H∗ by the finite dual A◦ of A. This decomposition is then further analysed using the Cartier–Gabriel–Kostant theorem to obtain component Hopf subalgebras of H◦ mapping onto the classical components of A◦. The detailed consequences for a number of families of examples are then studied.

Item Type:Articles
Status:Early Online Publication
Refereed:Yes
Glasgow Author(s) Enlighten ID:Couto, Miguel and Brown, Professor Ken
Authors: Brown, K. A., Couto, M., and Jahn, A.
College/School:College of Science and Engineering > School of Mathematics and Statistics
Journal Name:Glasgow Mathematical Journal
Publisher:Cambridge University Press
ISSN:0017-0895
ISSN (Online):1469-509X
Published Online:21 March 2022
Copyright Holders:Copyright © 2022 The Authors
First Published:First published in Glasgow Mathematical Journal 2022
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
300872Aspects of noncommutative geometry and noncommutative algebraKenneth BrownLeverhulme Trust (LEVERHUL)EM-2017-081\9M&S - Mathematics