2024/01/23 by Cedo, Ferran, Okninski, Jan
#16T25 #20B15 #20F16 #FOS: Mathematics #Group Theory (math.GR) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2401.12904
A new class of indecomposable, irretractable, involutive, non-degenerate set-theoretic solutions of the Yang--Baxter equation is constructed. This class complements the class of such solutions constructed in \citeCO22 and together they generalize the class of solutions described in \cite[Theorem 4.7CO21. Necessary and sufficient conditions are found in order that these new solutions are simple. For a rich subclass of these solutions the structure of their permutation groups, considered as left braces, is determined. In particular, these results answer a question stated in \citeCO21. In the finite case, all these solutions have square cardinality. A new class of finite simple solutions of non-square cardinality such that their permutation groups are simple left braces is also constructed.