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The structure of Hopf algebras giving Hopf-Galois structures on Quaternionic extensions

Truman, Paul; Taylor, Stuart

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Authors

Stuart Taylor



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.

Acceptance Date Dec 11, 2018
Publication Date Mar 5, 2019
Publicly Available Date Mar 28, 2024
Journal New York Journal of Mathematics
Print ISSN 1076-9803
Pages 219-237
Keywords Hopf Galois structure, Hopf algebra, Galois extension, Wedderburn-Artin decomposition
Publisher URL http://nyjm.albany.edu/j/2019/25-13.html

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