A characterization of finite multipermutation solutions of the Yang-Baxter equation

We prove that a finite non-degenerate involutive set-theoretic solution (X, r) of the Yang{Baxter equation is a multipermutation solution if and only if its structure group G(X, r) admits a left ordering or equivalently it is poly-Z. © 2018 Universitat Autonoma de Barcelona. All rights reserved.

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Detalles Bibliográficos
Autores principales: Bachiller, D., Cedó, F., Vendramin, L.
Formato: JOUR
Materias:
Brace
Ordered groups
Poly-(infinite cyclic) group
Set-theoretic solution
Yang-Baxter equation
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_02141493_v62_n2_p641_Bachiller
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_02141493_v62_n2_p641_Bachiller
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spelling todo:paper_02141493_v62_n2_p641_Bachiller2023-10-03T15:10:12Z A characterization of finite multipermutation solutions of the Yang-Baxter equation Bachiller, D. Cedó, F. Vendramin, L. Brace Ordered groups Poly-(infinite cyclic) group Set-theoretic solution Yang-Baxter equation We prove that a finite non-degenerate involutive set-theoretic solution (X, r) of the Yang{Baxter equation is a multipermutation solution if and only if its structure group G(X, r) admits a left ordering or equivalently it is poly-Z. © 2018 Universitat Autonoma de Barcelona. All rights reserved. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_02141493_v62_n2_p641_Bachiller
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Brace
Ordered groups
Poly-(infinite cyclic) group
Set-theoretic solution
Yang-Baxter equation
spellingShingle Brace
Ordered groups
Poly-(infinite cyclic) group
Set-theoretic solution
Yang-Baxter equation
Bachiller, D.
Cedó, F.
Vendramin, L.
A characterization of finite multipermutation solutions of the Yang-Baxter equation
topic_facet Brace
Ordered groups
Poly-(infinite cyclic) group
Set-theoretic solution
Yang-Baxter equation
description We prove that a finite non-degenerate involutive set-theoretic solution (X, r) of the Yang{Baxter equation is a multipermutation solution if and only if its structure group G(X, r) admits a left ordering or equivalently it is poly-Z. © 2018 Universitat Autonoma de Barcelona. All rights reserved.
format JOUR
author Bachiller, D.
Cedó, F.
Vendramin, L.
author_facet Bachiller, D.
Cedó, F.
Vendramin, L.
author_sort Bachiller, D.
title A characterization of finite multipermutation solutions of the Yang-Baxter equation
title_short A characterization of finite multipermutation solutions of the Yang-Baxter equation
title_full A characterization of finite multipermutation solutions of the Yang-Baxter equation
title_fullStr A characterization of finite multipermutation solutions of the Yang-Baxter equation
title_full_unstemmed A characterization of finite multipermutation solutions of the Yang-Baxter equation
title_sort characterization of finite multipermutation solutions of the yang-baxter equation
url http://hdl.handle.net/20.500.12110/paper_02141493_v62_n2_p641_Bachiller
work_keys_str_mv AT bachillerd acharacterizationoffinitemultipermutationsolutionsoftheyangbaxterequation
AT cedof acharacterizationoffinitemultipermutationsolutionsoftheyangbaxterequation
AT vendraminl acharacterizationoffinitemultipermutationsolutionsoftheyangbaxterequation
AT bachillerd characterizationoffinitemultipermutationsolutionsoftheyangbaxterequation
AT cedof characterizationoffinitemultipermutationsolutionsoftheyangbaxterequation
AT vendraminl characterizationoffinitemultipermutationsolutionsoftheyangbaxterequation
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