Cocyclic braces and indecomposable cocyclic solutions of the Yang-Baxter equation
Přemysl Jedlička, Agata Pilitowska, Anna Zamojska-Dzienio
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}.
Topics & Concepts
Indecomposable modulePermutation (music)MathematicsSet (abstract data type)Pure mathematicsCombinatoricsPhysicsComputer scienceAcousticsProgramming languageAlgebraic structures and combinatorial modelsAdvanced Topics in AlgebraFinite Group Theory Research