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arXiv · 2001.10967

Radical and weight of skew braces and their applications to structure groups of solutions of the Yang-Baxter equation

E. Jespers·Ł. Kubat·A. Van Antwerpen·L. Vendramin
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Abstract

We define the radical and weight of a skew left brace and provide some basic properties of these notions. In particular, we obtain a Wedderburn type decomposition for Artinian skew left braces. Furthermore, we prove analogues of a theorem of Wiegold, a theorem of Schur and its converse in the context of skew left braces. Finally, we apply these results to detect torsion in the structure group of a finite bijective non-degenerate set-theoretic solution of the Yang-Baxter equation.

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E. Jespers, Ł. Kubat, A. Van Antwerpen, L. Vendramin. 2020-01-29. Radical and weight of skew braces and their applications to structure groups of solutions of the Yang-Baxter equation. https://doi.org/10.1016/j.aim.2021.107767

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