A family of solutions of the Yang-Baxter equation

Abstract

A new method to construct involutive non-degenerate set-theoretic solutions $(X^n,r^{(n)})$ of the Yang-Baxter equation from an initial solution $(X,r)$ is given. Furthermore, the permutation group $\mathcal{G}(X^n,r^{(n)})$ associated to the solution $(X^n,r^{(n)})$ is isomorphic to a subgroup of $\mathcal{G}(X,r)$, and in many cases $\mathcal{G}(X^n,r^{(n)})\cong \mathcal{G}(X,r)$.