Abelian maps, bi-skew braces, and opposite pairs of {H}opf-{G}alois structures
| Autor: | Koch, Alan |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $G$ be a finite nonabelian group, and let $\psi:G\to G$ be a homomorphism with abelian image. We show how $\psi$ gives rise to two Hopf-Galois structures on a Galois extension $L/K$ with Galois group (isomorphic to) $G$; 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. Comment: Removed section on brace chains (will appear in a separate paper). New dihedral example given at the end |
| Databáze: | arXiv |
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