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math-ph2025
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…
math.GR2025
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…
math.RA2025
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 …