Date of Award

5-2017

Degree Type

Honors College Thesis

Department

Mathematics

First Advisor

Jiu Ding, Ph. D.

Advisor Department

Mathematics

Abstract

The Yang-Baxter equation is one that has been widely used and studied in areas such as statistical mechanics, braid groups, knot theory, and quantum mechanics. While many sets of solutions have been found for this equation, it is still an open problem. In this project, I solve the Yang-Baxter matrix equation that is similar in format to the Yang-Baxter equation. I try to solve the corresponding Yang-Baxter matrix equation, 𝐴𝑋𝐴=𝑋𝐴𝑋, where X is an unknown 𝑛π‘₯𝑛 matrix, and 𝐴=[0𝐼𝐼0] or [0βˆ’πΌβˆ’πΌ0], by using the Jordan canonical form to find infinitely many solutions.

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