Skew braces and the Yang–Baxter equation

Guarnieri, L.; Vendramin, L.

doi:10.1090/mcom/3161

Skew braces and the Yang–Baxter equation
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by L. Guarnieri and L. Vendramin PDF

Math. Comp. 86 (2017), 2519-2534 Request permission

Abstract:

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.

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