Simplicity of indecomposable set-theoretic solutions of the Yang–Baxter equation-Reference-Cited by-同舟云学术

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

Published:2022-03-01 Issue:2 Volume:34 Page:531-546
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Castelli Marco¹^ORCID,Mazzotta Marzia¹^ORCID,Stefanelli Paola¹^ORCID

Affiliation:

1. Dipartimento di Matematica e Fisica “Ennio De Giorgi” , Università del Salento , Via Provinciale Lecce-Arnesano, 73100 Lecce , Italy

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/forum-2021-0189/pdf

Reference37 articles.

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5. M. Castelli, F. Catino and P. Stefanelli, Indecomposable involutive set-theoretic solutions of the Yang–Baxter equation and orthogonal dynamical extensions of cycle sets, Mediterr. J. Math. 18 (2021), no. 6, Paper No. 246.

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