Actions of skew braces and set-theoretic solutions of the reflection equation. (English) Zbl 1470.16068
Summary: A skew brace, as introduced by L. Guarnieri and L. Vendramin [Math. Comput. 86, No. 307, 2519–2534 (2017; Zbl 1371.16037)], is a set with two group structures interacting in a particular way. When one of the group structures is abelian, one gets back the notion of brace as introduced by W. Rump [Algebra Discrete Math. 2006, No. 2, 127–137 (2006; Zbl 1164.81328)]. Skew braces can be used to construct solutions of the quantum Yang-Baxter equation. In this article, we introduce a notion of action of a skew brace, and show how it leads to solutions of the closely associated reflection equation.
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