English

Cocyclic braces and indecomposable cocyclic solutions of the Yang-Baxter equation

Rings and Algebras 2023-08-15 v1 Combinatorics

Abstract

We study indecomposable involutive set-theoretic solutions of the Yang-Baxter equation with cyclic permutation groups (cocyclic solutions). In particular, we show that there is no one-to-one correspondence between indecomposable cocyclic solutions and cocyclic braces which contradicts recent results in \cite{Rump21}.

Keywords

Cite

@article{arxiv.2107.12319,
  title  = {Cocyclic braces and indecomposable cocyclic solutions of the Yang-Baxter equation},
  author = {Přemysl Jedlička and Agata Pilitowska and Anna Zamojska-Dzienio},
  journal= {arXiv preprint arXiv:2107.12319},
  year   = {2023}
}