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Indecomposable set-theoretical solutions to the Yang-Baxter equation of size $p^2$

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arXiv:2403.18653v1 Announce Type: new
Abstract: The quantum Yang-Baxter equation is a braiding condition on complex vector spaces which is of high relevance in several fields of mathematics, such as knot theory and quantum group theory. A combinatorial approach is the investigation of set-theoretic solutions to the Yang--Baxter equation and their associated algebraic structures. In this article, we focus on indecomposable set-theoretic solutions to the Yang--Baxter equation. More specifically, we give a full classification of those which are of size $p^2$.

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