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arXiv · 2107.11104

Simplicity and finite primitive level of indecomposable set-theoretic solutions of the Yang-Baxter equation

Marco Castelli·Marzia Mazzotta·Paola Stefanelli
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Abstract

This paper aims to deepen the theory of bijective non-degenerate set-theoretic solutions of the Yang-Baxter equation, not necessarily involutive, by means of q-cycle sets. We entirely focus on the finite indecomposable ones among which we especially study two classes of current interest: the simple solutions and those having finite primitive level. In particular, we provide two group-theoretic characterizations of these solutions, involving their permutation groups. Finally, we deal with some open questions.

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Marco Castelli, Marzia Mazzotta, Paola Stefanelli. 2021-07-23. Simplicity and finite primitive level of indecomposable set-theoretic solutions of the Yang-Baxter equation. https://arxiv.org/abs/2107.11104

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