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arXiv · 2205.01572

Nilpotency of skew braces and multipermutation solutions of the Yang-Baxter equation

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

We study relations between different notions of nilpotency in the context of skew braces and applications to the structure of solutions to the Yang-Baxter equation. In particular, we consider annihilator nilpotent skew braces, an important class that turns out to be a brace-theoretic analog to the class of nilpotent groups. In this vein, several well-known theorems in group theory are proved in the more general setting of skew braces.

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E. Jespers, A. Van Antwerpen, L. Vendramin. 2022-05-03. Nilpotency of skew braces and multipermutation solutions of the Yang-Baxter equation. https://doi.org/10.1142/s021919972250064x

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