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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Detalles Bibliográficos
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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Sumario: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.