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arXiv · 2404.15929

Skew bracoids containing a skew brace

Ilaria Colazzo·Alan Koch·Isabel Martin-Lyons·Paul J. Truman
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Abstract

Skew bracoids have been shown to have applications in Hopf-Galois theory. We show that a certain family of skew bracoids correspond bijectively with left cancellative semibraces. A consequence of this correspondence is that skew bracoids in this family can be used to obtain and study solutions of the set-theoretic Yang--Baxter equation; we study this process and the resulting solutions. We give numerous examples of skew bracoids satisfying our hypothesis, drawing upon a variety of constructions in the literature.

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Ilaria Colazzo, Alan Koch, Isabel Martin-Lyons, Paul J. Truman. 2024-04-24. Skew bracoids containing a skew brace. https://arxiv.org/abs/2404.15929

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