Date of Award
Summer 8-2011
Degree Type
Masters Thesis
Degree Name
Master of Science (MS)
Department
Mathematics
Committee Chair
Joseph Kolibal
Committee Chair Department
Mathematics
Committee Member 2
C.S. Chen
Committee Member 2 Department
Mathematics
Committee Member 3
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/
Copyright
2011, Alexandru Cibotarica
Recommended Citation
Cibotarica, Alexandru, "An Examination of the Yang-Baxter Equation" (2011). Master's Theses. 208.
https://aquila.usm.edu/masters_theses/208