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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. |
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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. |
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Acknowledgements
N/A
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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
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