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

Stuart Taylor; Paul J Truman

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

Rings and Algebras 2018-12-06 v3

Authors: Stuart Taylor , Paul J Truman

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.

Keywords

galois extension quaternion group hopf-galois structure hopf algebra wedderburn-artin decomposition characteristic zero

Cite

@article{arxiv.1809.09497,
  title  = {The structure of Hopf algebras giving Hopf-Galois structures on Quaternionic extensions},
  author = {Stuart Taylor and Paul J Truman},
  journal= {arXiv preprint arXiv:1809.09497},
  year   = {2018}
}

Comments

15 pages, some arguments shortened, some more exposition included

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

Abstract

Keywords

Cite

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