8 papers
Retracts of degenerate solutions of the Yang-Baxter equation
Přemysl Jedlička, Agata Pilitowska
Most of the set-theoretical solutions of the Yang-Baxter equation studied in the past years were non-degenerate multipermutation solutions. For degenerate solutions, a correct defi…
Indecomposable non-degenerate 2-permutational solutions of the Yang-Baxter equation
Přemysl Jedlička, Agata Pilitowska
We present a complete characterization of all indecomposable non-degenerate, not necessarily involutive, solutions of the Yang-Baxter equation of multipermutation level~2. We show…
Indecomposable involutive solutions of the Yang-Baxter equation of multipermutation level 2 with non-abelian permutation group
Přemysl Jedlička, Agata Pilitowska
We give a complete characterization of all indecomposable involutive solutions of the Yang-Baxter equation of multipermutation level~2. In the first step we present a construction…
Central nilpotency of skew braces
Marco Bonatto, Přemysl Jedlička
Skew braces are algebraic structures related to the solutions of the set-theoretic quantum Yang-Baxter equation. We develop the central nilpotency theory for such algebraic structu…
Cocyclic braces and indecomposable cocyclic solutions of the Yang-Baxter equation
Přemysl Jedlička, Agata Pilitowska, Anna Zamojska-Dzienio
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…
Distributive biracks and solutions of the Yang-Baxter equation
Přemysl Jedlička, Agata Pilitowska, Anna Zamojska-Dzienio
We investigate a class of non-involutive solutions of the Yang-Baxter equation which generalize self-distributive (derived) solutions. In particular, we study generalized multiperm…