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arXiv · 2407.07907

Simple solutions of the Yang-Baxter equation of cardinality $p^n$

Ferran Cedo·Jan Okninski
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Abstract

For every prime number p and integer $n>1$, a simple, involutive, non-degenerate set-theoretic solution $(X,r$) of the Yang-Baxter equation of cardinality $|X| = p^n$ is constructed. Furthermore, for every non-(square-free) positive integer m which is not the square of a prime number, a non-simple, indecomposable, irretractable, involutive, non-degenerate set-theoretic solution $(X,r)$ of the Yang-Baxter equation of cardinality $|X| = m$ is constructed. A recent question of Castelli on the existence of singular solutions of certain type is also answered affirmatively.

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BibTeXRIS

Ferran Cedo, Jan Okninski. 2024-06-29. Simple solutions of the Yang-Baxter equation of cardinality $p^n$. https://arxiv.org/abs/2407.07907

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