Abelian fixed point free endomorphisms and the Yang-Baxter equation
Group Theory
2020-06-24 v1 Mathematical Physics
math.MP
Number Theory
Rings and Algebras
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.
Cite
@article{arxiv.2006.13196,
title = {Abelian fixed point free endomorphisms and the Yang-Baxter equation},
author = {Alan Koch and Laura Stordy and Paul J. Truman},
journal= {arXiv preprint arXiv:2006.13196},
year = {2020}
}
Comments
16 pages