TY - JOUR
T1 - Actions of skew braces and set-theoretic solutions of the reflection equation
AU - De Commer, Kenny
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85068171255&partnerID=8YFLogxK
U2 - 10.1017/S0013091519000129
DO - 10.1017/S0013091519000129
M3 - Article
SN - 0013-0915
VL - 62
SP - 1089
EP - 1113
JO - Proceedings of the Edinburgh Mathematical Society
JF - Proceedings of the Edinburgh Mathematical Society
IS - 4
ER -