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Simplicity of indecomposable set-theoretic solutions of the Yang–Baxter equation

  • Marco Castelli ORCID logo EMAIL logo , Marzia Mazzotta ORCID logo and Paola Stefanelli ORCID logo
From the journal Forum Mathematicum

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.


Communicated by Manfred Droste


Funding statement: This work was partially supported by Dipartimento di Matematica e Fisica “Ennio De Giorgi” – Università del Salento. The second and the third authors were partially supported by the ACROSS project ARS01_00702. The authors are members of GNSAGA (INdAM).

Acknowledgements

We thank the anonymous referee for his/her useful suggestions for improving the final organization of this paper.

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Received: 2021-07-23
Revised: 2021-12-16
Published Online: 2022-03-01
Published in Print: 2022-03-01

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