Abelian maps, bi-skew braces, and opposite pairs of Hopf-Galois structures

Author:

Koch Alan

Abstract

Let G G be a finite nonabelian group, and let ψ : G G \psi :G\to G be a homomorphism with abelian image. We show how ψ \psi gives rise to two Hopf-Galois structures on a Galois extension L / K L/K with Galois group (isomorphic to) G G ; one of these structures generalizes the construction given by a “fixed point free abelian endomorphism” introduced by Childs in 2013. We construct the skew left brace corresponding to each of the two Hopf-Galois structures above. We will show that one of the skew left braces is in fact a bi-skew brace, allowing us to obtain four set-theoretic solutions to the Yang-Baxter equation as well as a pair of Hopf-Galois structures on a (potentially) different finite Galois extension.

Publisher

American Mathematical Society (AMS)

Subject

General Medicine

Reference20 articles.

1. Counterexample to a conjecture about braces;Bachiller, David;J. Algebra,2016

2. Monogenic Hopf orders and associated orders of valuation rings;Byott, Nigel P.;J. Algebra,2004

3. Quasi-inverse endomorphisms;Caranti, A.;J. Group Theory,2013

4. Counting Hopf Galois structures on non-abelian Galois field extensions;Carnahan, Scott;J. Algebra,1999

5. Bi-skew braces and Hopf Galois structures;Childs, Lindsay N.;New York J. Math.,2019

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