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

Jedlička, Přemysl; Pilitowska, Agata; Zamojska-Dzienio, Anna

doi:10.1090/proc/15962

Cocyclic braces and indecomposable cocyclic solutions of the Yang-Baxter equation
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by Přemysl Jedlička, Agata Pilitowska and Anna Zamojska-Dzienio PDF

Proc. Amer. Math. Soc. 150 (2022), 4223-4239 Request permission

Abstract:

We study indecomposable involutive set-theoretic solutions of the Yang-Baxter equation with cyclic permutation groups (cocyclic solutions). We give a complete system of three invariants for finite non-isomorphic solutions of this type and use this construction to enumerate all of them.

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