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}
}