Skew braces and the Yang-Baxter equation

Braces were introduced by Rump to study non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation. We generalize Rump's braces to the non-commutative setting and use this new structure to study not necessarily involutive non-degenerate set-theoretical solutions of the Yang-B...

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Autores principales: Guarnieri, L., Vendramin, L.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00255718_v86_n307_p2519_Guarnieri
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00255718_v86_n307_p2519_Guarnieri2023-10-03T14:36:15Z Skew braces and the Yang-Baxter equation Guarnieri, L. Vendramin, L. Braces were introduced by Rump to study non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation. We generalize Rump's braces to the non-commutative setting and use this new structure to study not necessarily involutive non-degenerate set-theoretical solutions of the Yang-Baxter equation. Based on results of Bachiller and Catino and Rizzo, we develop an algorithm to enumerate and construct classical and non-classical braces of small size up to isomorphism. This algorithm is used to produce a database of braces of small size. The paper contains several open problems, questions and conjectures. © 2017 American Mathematical Society. Fil:Vendramin, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00255718_v86_n307_p2519_Guarnieri
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description Braces were introduced by Rump to study non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation. We generalize Rump's braces to the non-commutative setting and use this new structure to study not necessarily involutive non-degenerate set-theoretical solutions of the Yang-Baxter equation. Based on results of Bachiller and Catino and Rizzo, we develop an algorithm to enumerate and construct classical and non-classical braces of small size up to isomorphism. This algorithm is used to produce a database of braces of small size. The paper contains several open problems, questions and conjectures. © 2017 American Mathematical Society.
format JOUR
author Guarnieri, L.
Vendramin, L.
spellingShingle Guarnieri, L.
Vendramin, L.
Skew braces and the Yang-Baxter equation
author_facet Guarnieri, L.
Vendramin, L.
author_sort Guarnieri, L.
title Skew braces and the Yang-Baxter equation
title_short Skew braces and the Yang-Baxter equation
title_full Skew braces and the Yang-Baxter equation
title_fullStr Skew braces and the Yang-Baxter equation
title_full_unstemmed Skew braces and the Yang-Baxter equation
title_sort skew braces and the yang-baxter equation
url http://hdl.handle.net/20.500.12110/paper_00255718_v86_n307_p2519_Guarnieri
work_keys_str_mv AT guarnieril skewbracesandtheyangbaxterequation
AT vendraminl skewbracesandtheyangbaxterequation
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