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arXiv · 1809.09497

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

Stuart Taylor·Paul J Truman
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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 zero we also determine which of these Hopf algebras are isomorphic as $ F $-algebras and explicitly compute their Wedderburn-Artin decompositions.

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Stuart Taylor, Paul J Truman. 2018-09-25. The structure of Hopf algebras giving Hopf-Galois structures on Quaternionic extensions. https://arxiv.org/abs/1809.09497

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