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/
","abstract_html":"<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>","abstract_has_math":false,"creators":["Cibotarica, Alexandru"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Masters Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Joseph Kolibal","C.S. Chen","James V. Lambers"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-08-01T07:00:00Z","date_published":"2011-08-01T07:00:00Z","updated_at":"2026-07-24T05:44:41Z","subjects":["Yang-Baxter equation","mathematics","physics","Applied Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://aquila.usm.edu/masters_theses/208","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Joseph Kolibal","C.S. Chen","James V. Lambers"]},{"key":"dc:creator","label":"Author","values":["Cibotarica, Alexandru"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-08-12T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Yang-Baxter equation","mathematics","physics","Applied Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://aquila.usm.edu/masters_theses/208"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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/
"]},{"key":"dc:title","label":"Title","values":["An Examination of the Yang-Baxter Equation"]}]}],"canonical_facts":{"dc:contributor":["Joseph Kolibal","C.S. Chen","James V. Lambers"],"dc:creator":["Cibotarica, Alexandru"],"dc:date.available":["2016-08-12T07:00:00Z"],"dc:description.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/
"],"dc:identifier":["https://aquila.usm.edu/masters_theses/208"],"dc:subject":["Yang-Baxter equation","mathematics","physics","Applied Mathematics"],"dc:title":["An Examination of the Yang-Baxter Equation"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Masters Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T05:44:41Z"}