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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.

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

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