Solutions to the matrix Yang-Baxter equation

2022/09/10 by Mukherjee, Himadri, M, Askar Ali
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2209.04605

Abstract

In this article, we give a few classes of solutions for the Yang-Baxter type matrix equation, AXA=XAX. We provide all solutions for the cases when A is equivalent to a Jordan block or has precisely two Jordan blocks. We also have given a few general properties of the solutions of the YB-equation.

Related

• Solutions to a system of Yang-Baxter matrix equations
• Anti-commuting Solutions of the Yang-Baxter-like Matrix Equation
• Explicit Solutions of the Singular Yang--Baxter-like Matrix Equation and Their Numerical Computation
• Jordan Triple Systems and Yang-Baxter Equation
• Involutive solutions of the Yang-Baxter-like matrix equation -- theory\n and algorithms