New simple solutions of the Yang-Baxter equation and solutions associated to simple left braces
Quantum Algebra
2021-12-15 v1
Abstract
Involutive non-degenerate set theoretic solutions of the Yang-Baxter equation are considered, with a focus on finite solutions. A rich class of indecomposable and irretractable solutions is determined and necessary and sufficient conditions are found in order that these solutions are simple. Then a link between simple solutions and simple left braces is established, that allows us to construct more examples of simple solutions. In particular, the results answer some problems stated in the recent paper [13].
Cite
@article{arxiv.2112.07271,
title = {New simple solutions of the Yang-Baxter equation and solutions associated to simple left braces},
author = {Ferran Cedó and Jan Okniński},
journal= {arXiv preprint arXiv:2112.07271},
year = {2021}
}
Comments
arXiv admin note: text overlap with arXiv:2012.08400