Involutive solutions of the Yang-Baxter-like matrix equation -- theory and algorithms

Abstract

We find all explicit involutive solutions $X\in {\mathbb{C}}^{n\times n}$ of the Yang-Baxter-like matrix equation $AXA=XAX$, where $A\in {\mathbb{C}}^{n\times n}$ is a given involutory matrix. The construction is algorithmic.