THE YANG-BAXTER MATRIX EQUATION FOR INVOLUTIONS

摘要

In this paper we find all involutive solutions X is an element of C-n Chi n of the Yang-Baxter matrix equa-tion AXA = XAX, where A is an element of C-n Chi n is a given involutory matrix. The construction is algorithmic. It is based on the concept of quadratic matrices. Algorithms for generating concrete involutive solutions of the Yang-Baxter matrix equation AXA = XAX are also presented along with several examples.