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Truman, PJ and Taylor, S (2019) The structure of Hopf algebras giving Hopf-Galois structures on Quaternionic extensions. New York Journal of Mathematics, 25. pp. 219-237. ISSN 1076-9803
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HGS on Quaternion Extensions Final.pdf - Accepted Version
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Official URL: http://nyjm.albany.edu/j/2019/25-13.html
Abstract
Let L/F be a Galois extension of fields with Galois group isomorphic to the quaternion group of order 8. We describe all of the Hopf-Galois structures admitted by L/F, and determine which of the Hopf algebras that appear are isomorphic as Hopf algebras. In the case that F has characteristic not equal to 2 we also determine which of these Hopf algebras are isomorphic as F-algebras and explicitly compute their Wedderburn-Artin decompositions.
Item Type: | Article |
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Additional Information: | This is the accepted author manuscript (AAM). The final published version (version of record) is available online via the website of the New York Journal of Mathematics at http://nyjm.albany.edu/nyjm.html - please refer to any applicable terms of use of the publisher. |
Uncontrolled Keywords: | Hopf Galois structure, Hopf algebra, Galois extension, Wedderburn-Artin decomposition |
Subjects: | Q Science > QA Mathematics |
Divisions: | Faculty of Natural Sciences > School of Computing and Mathematics |
Depositing User: | Symplectic |
Date Deposited: | 12 Dec 2018 11:33 |
Last Modified: | 05 Mar 2020 01:30 |
URI: | https://eprints.keele.ac.uk/id/eprint/5575 |