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arXiv · 2303.15154

Skew left braces and 2-reductive solutions of the Yang-Baxter equation

Přemysl Jedlička·Agata Pilitowska
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Abstract

We study 2-reductive non-involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation. We give a combinatorial construction of any such solution of any (even infinite) size. We also prove that solutions associated to a skew left brace are 2-reductive if and only if the skew left brace is nilpotent of class 2. Moreover, all such skew left braces are actually bi-skew left braces. We focus on these structures and we give several equivalent properties characterizing solutions associated to bi-skew left braces.

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Přemysl Jedlička, Agata Pilitowska. 2023-03-27. Skew left braces and 2-reductive solutions of the Yang-Baxter equation. https://arxiv.org/abs/2303.15154

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