6 citations · 16 across the 5 of their papers we have counts for
5 papers
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…
Deformed solutions of the Yang-Baxter equation associated to dual weak braces
Marzia Mazzotta, Bernard Rybołowicz, 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…
Near braces and p-deformed braided groups
Anastasia Doikou, Bernard Rybolowicz
Motivated by recent findings on the derivation of parametric non-involutive solutions of the Yang-Baxter equation we reconstruct the underlying algebraic structures, called near br…
Biunit pairs in semiheaps and associated semigroups
Bernard Rybołowicz, Carlos Zapata-Carratalá
Biunit pairs are introduced as pairs of elements in a semiheap that generalize the notion of unit. Families of functions generalizing involutions and conjugations, called switches…
Novel non-involutive solutions of the Yang-Baxter equation from (skew) braces
Anastasia Doikou, Bernard Rybolowicz
We produce novel non-involutive solutions of the Yang-Baxter equation coming from (skew) braces. These solutions are generalisations of the known ones coming from braces and skew b…