Date of Award

Summer 8-2011

Degree Type

Masters Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

Committee Chair

Dr. Joseph Kolibal

Committee Chair Department

Mathematics

Committee Member 2

Dr. C.S. Chen

Committee Member 2 Department

Mathematics

Committee Member 3

Dr. James V. Lambers

Committee Member 3 Department

Mathematics

Abstract

The Yang-Baxter equation has been extensively studied due to its application in numerous fields of mathematics and physics. This thesis sets out to analyze the equation from the viewpoint of the algebraic product of matrices, i.e., the composition of linear maps, with the intent of characterizing the solutions of the Yang-Baxter equation.

We begin by examining the simple case of 22 matrices where it is possible to fully characterize the solutions. We connect the Yang-Baxter equation to the Cecioni-Frobenius Theorem and focus on obtaining solutions to the Yang-Baxter equation for special matrices where solutions are more easily found. Finally, we derive a fixed point iteration algorithm to determine the Yang-Baxter complement of a given matrix, if it exists.

Doctoral dissertation: http://aquila.usm.edu/dissertations/103/

Share

COinS