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New York Journal of Mathematics
Volume 26 (2020), 1473-1492

  

Alan Koch, Laura Stordy, and Paul J. Truman

Abelian fixed point free endomorphisms and the Yang-Baxter equation

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Published: December 8, 2020.
Keywords: Yang-Baxter equation; skew left braces; Hopf-Galois extensions.
Subject: 16T25, 16T05, 20N99.

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.

Acknowledgements

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Author information

Alan Koch:
Department of Mathematics
Agnes Scott College
141 E. College Ave.
Decatur, GA 30030, USA

akoch@agnesscott.edu

Laura Stordy:
School of Mathematics
Georgia Institute of Technology
686 Cherry St NW
Atlanta, GA 30332, USA

lstordy3@gatech.edu

Paul J. Truman:
School of Computing and Mathematics
Keele University
Staffordshire, ST5 5BG, UK

p.j.truman@keele.ac.uk