The following paper has been published:
El siguiente artículo ha sido publicado:
El següent article ha sigut publicat:
A. Ballester-Bolinches, R. Esteban-Romero, N. Fuster-Corral, H. Meng.
The Structure Group and the Permutation Group of a Set-Theoretic Solution of the Quantum Yang–Baxter Equation.
Mediterr. J. Math, 18: Article number 145, 2021.
We describe the left brace structure of the structure group and the permutation group associated with an involutive, non-degenerate set-theoretic solution of the quantum Yang–Baxter equation using the Cayley graph of its permutation group with respect to its natural generating system. We use our descriptions of the additions in both braces to obtain new properties of the structure and the permutation groups and to recover some known properties of these groups in a more transparent way.
2020 Mathematics Subject Classification: 16T25, 05C25, 20F05, 20F65
Keywords: left brace, Yang-Baxter equation, Cayley graph, structure group.