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

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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

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