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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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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
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

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