Brown, K.A. , Couto, M. and Jahn, A. (2023) The finite dual of commutative-by-finite Hopf algebras. Glasgow Mathematical Journal, 65(1), pp. 62-89. (doi: 10.1017/S0017089522000052)
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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 |
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Status: | Published |
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 65(1): 62-89 |
Publisher Policy: | Reproduced under a Creative Commons License |
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