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

2021/07/23 by Castelli, Marco, Mazzotta, Marzia, Stefanelli, Paola
#16T25 #20E22 #20N02 #81R50 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2107.11104

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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