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Actions of skew braces and set-theoretic solutions of the reflection equation

Part of: Hopf algebras, quantum groups and related topics Other generalizations of groups

Published online by Cambridge University Press:  25 June 2019

K. De Commer
K. De Commer*
Affiliation:
Vakgroep Wiskunde, Vrije Universiteit Brussel (VUB), B-1050 Brussels, Belgium (kenny.de.commer@vub.be)
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Abstract

A skew brace, as introduced by L. Guarnieri and L. Vendramin, 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. 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.

Keywords

reflection equationYang–Baxter equationbracesbraided groups

MSC classification

Primary: 16T25: Yang-Baxter equations
Secondary: 20N99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 4 , November 2019 , pp. 1089 - 1113
Copyright
Copyright © Edinburgh Mathematical Society 2019 

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