Decomposition theorems for involutive solutions to the Yang-Baxter equation
Exactly Solvable and Integrable Systems
2022-12-15 v2 Group Theory
Quantum Algebra
Abstract
Motivated by the proof of Rump of a conjecture of Gateva-Ivanova on the decomposability of square-free solutions to the Yang-Baxter equation, we present several other decomposability theorems based on the cycle structure of a certain permutation associated with the solution.
Keywords
Cite
@article{arxiv.2101.04239,
title = {Decomposition theorems for involutive solutions to the Yang-Baxter equation},
author = {S. Ramírez and L. Vendramin},
journal= {arXiv preprint arXiv:2101.04239},
year = {2022}
}
Comments
10 pages. Accepted for publication in Int. Math. Res. Not. IMRN