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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.GR2020
Indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level 2 with abelian permutation group
Přemysl Jedlička, Agata Pilitowska, Anna Zamojska-Dzienio
We present a construction of all finite indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level at most 2 with abelian permutation group. As a c…
math.GR2018
Knot-theoretic ternary groups
Maciej Niebrzydowski, Agata Pilitowska, Anna Zamojska-Dzienio
We describe various properties and give several characterizations of ternary groups satisfying two axioms derived from the third Reidemeister move in knot theory. Using special att…