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arXiv · 2107.12319

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

Přemysl Jedlička·Agata Pilitowska·Anna Zamojska-Dzienio
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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}.

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Přemysl Jedlička, Agata Pilitowska, Anna Zamojska-Dzienio. 2021-07-26. Cocyclic braces and indecomposable cocyclic solutions of the Yang-Baxter equation. https://doi.org/10.1090/proc%2F15962

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