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.
Simplicity of indecomposable set-theoretic solutions of the Yang–Baxter equation
Castelli, Marco;Mazzotta, Marzia;Stefanelli, Paola
2022-01-01
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 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.File in questo prodotto:
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