Almost classical skew bracoids

Isabel Martin-Lyons

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arXiv · 2412.10268

Almost classical skew bracoids

Isabel Martin-Lyons

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Abstract

We investigate two sub-classes of skew bracoids, the first consists of those we term almost a brace, meaning the multiplicative group decomposes as a certain semi-direct product, and then those that are almost classical, which additionally specifies the relationship between the multiplicative group and the additive. Skew bracoids with these properties have applications in Hopf-Galois theory, in particular for questions concerning the Hopf-Galois correspondence, and can also yield solutions to the set-theoretic Yang-Baxter equation. We use this skew bracoid perspective to give a new construction building on the induced Hopf-Galois structures of Crespo, Rio and Vela, recover a result of Greither and Pareigis on the Hopf-Galois correspondence, and examine the solutions that arise from skew bracoids, in particular where more than one solution may be drawn from a single skew bracoid.

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Isabel Martin-Lyons. 2024-12-23. Almost classical skew bracoids. https://arxiv.org/abs/2412.10268

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