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

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.

25 pages; accepted on Forum Math.: this is a preprint-version which includes some other results

References in corpus (5)

• Semigroups of I-type
• The retraction relation for biracks
• Involutive latin solutions of the Yang-Baxter equation
• A combinatorial approach to noninvolutive set-theoretic solutions of the Yang-Baxter equation
• Indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level 2 with abelian permutation group