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math.QA2024
Deformed solutions of the Yang-Baxter equation associated to dual weak braces
Marzia Mazzotta, Bernard RyboÅowicz, Paola Stefanelli
A dual weak brace is an algebraic structure including skew braces and giving rise to a set-theoretic solution of the Yang-Baxter equation. We show that…
math.QA2024
Quandles as pre-Lie skew braces, set-theoretic Hopf algebras & universal R-matrices
Anastasia Doikou, Bernard Rybolowicz, Paola Stefanelli
We present connections between left non-degenerate solutions of the set-theoretic braid equation and left shelves using Drinfel'd homomorphisms. We generalize the notion of affine…