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Mathematics

The Yang-Baxter Equation and Integrable Systems

Keith McHugh ('12); Peter Fedak ('13 HMC); Sundeep Sampath*; Mentor: Gizem Karaali
*Claremont Graduate University, Claremont, CA

Abstract:  Integrable systems are examples of classical mechanics which can be fully understood mathematically; they exist in relatively simple phase space. The classical Yang-Baxter equation is an algebraic equation whose solutions can be translated into integrable systems. This process is well-understood in the non-graded case. Our project examines methods of constructing integrable systems from solutions of the graded classical Yang-Baxter equations by using work done with Lie superalgebras by following the work of Zhang, Gould, and Bracken (1991).
Funding Provided by: Pomona College Mathemathic Dept.

Research at Pomona