Solutions to the constant Yang-Baxter equation in all dimensions

Abstract

We will present solutions to the constant Yang-Baxter equation, in any dimension $n$. More precisely, for any $n$, we will create an infinite family of $n^2$ by $n^2$ matrices which are solutions to the constant Yang-Baxter equation. The total number of non-vanishing entries of such a matrix is $4n^2$ for $n$ even, and $4(n-1)(n)+1$ for $n$ odd. We will also present the unitary conditions for those matrices. Moreover, we discuss the entangling property of those matrices.