Abelian fixed point free endomorphisms and the Yang-Baxter equation

Koch, Alan; Stordy, Laura; Truman, Paul J.

Abstract

We obtain a simple family of solutions to the set-theoretic Yang-Baxter equation, one which depends only on considering special endomorphisms of a finite group. We show how such an endomorphism gives rise to two non-degenerate solutions to the Yang-Baxter equation, solutions which are inverse to each other. We give concrete examples using dihedral, alternating, symmetric, and metacyclic groups.

Citation

Koch, A., Stordy, L., & Truman, P. J. (2020). Abelian fixed point free endomorphisms and the Yang-Baxter equation

• Acceptance Date: Oct 13, 2020
• Publication Date: Dec 8, 2020
• Journal: New York Journal of Mathematics
• Print ISSN: 1076-9803
• Pages: 1473-1492
• Publisher URL: https://www.emis.de/journals/NYJM/j/2020/26-58.html