Paola Stefanelli

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 the class of simple solutions. In particular, we provide a group-theoretic characterization of these solutions, including their permutation groups. Finally, we deal with some open questions.