On Yang-Baxter groups

Abstract

A group is said to be an involutive Yang-Baxter group, or simply an IYB-group, if it is isomorphic to the permutation group of an involutive, non-degenerate set-theoretic solution of the Yang-Baxter equation. In this paper, Yang-Baxter groups (YB-groups for short) associated with not necessarily involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation are introduced and studied. Sufficient conditions for a group that can be factorised as a product of two YB-groups to be a YB-group are provided. Some earlier results for finite IYB-groups are also generalised for arbitrary (non-necessarily finite) YB-groups as a consequence of our main theorem.

Mathematics Subject Classification (2020):

• Primary: 81R50
• Secondary: 20F29
• 20B35
• 20F16
• 20C05
• 16S34
• 16T25

Key words:

• Skew left brace
• Yang-Baxter equation
• non-degenerate solution
• Yang-Baxter group