Keele Research Repository
Explore the Repository
Truman, PJ and Koch, A (2022) Skew left braces and isomorphism problems for Hopf-Galois structures on Galois extensions. Journal of Algebra and Its Applications. ISSN 0219-4988
Braces and Isomorphism Problems 2021.pdf - Accepted Version
Available under License Creative Commons Attribution Non-commercial.
Download (313kB) | Preview
Abstract
Given a finite group G, we study certain regular subgroups of the group of permutations of G, which occur in the classification theories of two types of algebraic objects: skew left braces with multiplicative group isomorphic to G and Hopf-Galois structures admitted by a Galois extension of fields with Galois group isomorphic to G. We study the questions of when two such subgroups yield isomorphic skew left braces or Hopf-Galois structures involving isomorphic Hopf algebras. In particular, we show that in some cases the isomorphism class of the Hopf algebra giving a Hopf-Galois structure is determined by the corresponding skew left brace. We investigate these questions in the context of a variety of existing constructions in the literature. As an application of our results we classify the isomorphically distinct Hopf algebras that give Hopf-Galois structures on a Galois extension of degree pq for p > q prime numbers.
Item Type: | Article |
---|---|
Additional Information: | The final version of this article and all relevant information related to it, including copyrights, can be found on the publisher website. |
Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics Q Science > QC Physics T Technology > T Technology (General) |
Divisions: | Faculty of Natural Sciences > School of Computing and Mathematics |
Depositing User: | Symplectic |
Date Deposited: | 12 Jan 2022 11:13 |
Last Modified: | 15 Apr 2023 01:30 |
URI: | https://eprints.keele.ac.uk/id/eprint/10487 |