2021/12/14 by Ferran Cedó, Cedó, Ferran, Jan Okniński +1 · 1 citation
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA
paper · pdf · doi:10.48550/arxiv.2112.07271
arXiv admin note: text overlap with arXiv:2012.08400
arxiv created 2021/12/14 · arxiv updated 2021/12/15
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].