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arXiv · 1511.03171

Skew braces and the Yang-Baxter equation

L. Guarnieri·L. Vendramin
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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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BibTeXRIS

L. Guarnieri, L. Vendramin. 2016-03-16. Skew braces and the Yang-Baxter equation. https://doi.org/10.1090/mcom%2F3161

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