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arXiv · 2307.03540

Solutions of the Yang-Baxter equation and strong semilattices of skew braces

Francesco Catino·Marzia Mazzotta·Paola Stefanelli
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Abstract

We prove that any set-theoretic solution of the Yang-Baxter equation associated to a dual weak brace is a strong semilattice of non-degenerate bijective solutions. This fact makes use of the description of any dual weak brace $S$ we provide in terms of strong semilattice $Y$ of skew braces $B_\alpha$, with $\alpha \in Y$. Additionally, we describe the ideals of $S$ and study its nilpotency by correlating it to that of each skew brace $B_\alpha$.

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Francesco Catino, Marzia Mazzotta, Paola Stefanelli. 2023-07-07. Solutions of the Yang-Baxter equation and strong semilattices of skew braces. https://doi.org/10.1007/s00009-024-02611-6

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