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Abelian fixed point free endomorphisms and the Yang-Baxter equation

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

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Authors

Alan Koch

Laura Stordy



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.

Acceptance Date Oct 13, 2020
Publication Date Dec 8, 2020
Publicly Available Date Mar 28, 2024
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

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