Solutions to the matrix Yang-Baxter equation
Himadri Mukherjee, Askar Ali M
TL;DR
This paper classifies solutions to the matrix Yang-Baxter equation for specific matrix forms, providing explicit solutions when matrices are Jordan blocks or have two Jordan blocks, and discusses general properties of these solutions.
Contribution
It offers a complete classification of solutions for matrices equivalent to Jordan blocks or with two Jordan blocks, advancing understanding of the matrix Yang-Baxter equation.
Findings
All solutions for matrices equivalent to a Jordan block.
Solutions for matrices with exactly two Jordan blocks.
General properties of solutions to the Yang-Baxter matrix equation.
Abstract
In this article, we give a few classes of solutions for the Yang-Baxter type matrix equation, . We provide all solutions for the cases when 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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Matrix Theory and Algorithms · Algebraic structures and combinatorial models