Research Article

On Yang-Baxter groups

Published in: Quaestiones Mathematicae
Volume 46 , issue 7 , 2023 , pages: 1273–1281

DOI: 10.2989/16073606.2022.2073921

Author(s): A. Ballester-Bolinches Guangdong University of Education, People’s Republic of China , R. Esteban-Romero Universitat de València, Spain , P. Jiménez-Seral Universidad de Zaragoza, Spain , V. Pérez-Calabuig Universitat de València, Spain

Keywords: Primary: 81R50 , Secondary: 20F29 , 20B35 , 20F16 , 20C05 , 16S34 , 16T25 , Skew left brace , Yang-Baxter equation , non-degenerate solution , Yang-Baxter group

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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.

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