A note on set theoretical solutions of the Yang-Baxter equation with trivial retraction
Rings and Algebras
2023-07-28 v2 Group Theory
Quantum Algebra
Abstract
We show that every finite non-degenerate set theoretical solution to the YBE whose retraction is a flip linearizes to a twist of the flip solution by roots of unity. This generalizes a result of Gateva-Ivanova and Majid. To prove the result we use a new invariant associated to a solution, its Lie algebra. We show also that a solution retracts to a flip solution if and only if its Lie algebra is abelian.
Cite
@article{arxiv.2110.03988,
title = {A note on set theoretical solutions of the Yang-Baxter equation with trivial retraction},
author = {Pablo Zadunaisky},
journal= {arXiv preprint arXiv:2110.03988},
year = {2023}
}
Comments
9 pages. Comments welcome. To be published in the JPAA