An Examination of the Yang-Baxter Equation

<p>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.</p> <p>We begin by examining the simple case of 2<strong></strong>2 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.</p> <p>Doctoral dissertation:<a href="http://aquila.usm.edu/dissertations/103/"> http://aquila.usm.edu/dissertations/103/</a></p>

Name thesis:degree_name

Master of Science (MS)

Level thesis:degree_level

Masters Thesis

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2011

Author dc:creator

• Cibotarica, Alexandru

Contributors dc:contributor

• Joseph Kolibal
• C.S. Chen
• James V. Lambers

• Yang-Baxter equation
• mathematics
• physics
• Applied Mathematics

Repository record dc:identifier

https://aquila.usm.edu/masters_theses/208

OAI identifier oai:identifier

oai:aquila.usm.edu:masters_theses-1237