English

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.

Keywords

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

R2 v1 2026-06-23T16:33:54.852Z