5 papers
Retracts of degenerate solutions of the Yang-Baxter equation
PÅemysl JedliÄka, 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
PÅemysl JedliÄka, 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…
Associative Pentagon Algebras
Marzia Mazzotta, Agata Pilitowska
A set-theoretic solution to the Pentagon Equation can be described as a \emph{pentagon} algebra such that is a semigroup and the operations …
Diagonals of solutions of the Yang-Baxter equation
Premysl Jedlicka, Agata Pilitowska
We study the diagonal mappings in non-involutive set-theoretic solutions of the Yang-Baxter equation. We show that, for non-degenerate solutions, they are commuting bijections. Thi…
Non-involutive solutions of the Yang-Baxter equation of multipermutation level 2
Jan Hora, Premysl Jedlicka, Agata Pilitowska
We study non-degenerate set-theoretic solutions of the Yang-Baxter equation of multipermutation level 2 which are not 2-reductive. We describe an effective way of constructing such…