2025/08/25 by Jedlička, Přemysl, Pilitowska, Agata
#20E07 #FOS: Mathematics #Group Theory (math.GR) #Primary: 16T25. Secondary: 20B35
paper · doi:10.48550/arxiv.2508.17981
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 that every such solution is a homomorphic image of a special, ``largest'' solution called the universal one. On the other hand we prove that there is much simpler description. At first, on the product of a group Zn2 and an abelian group G, we construct some family of indecomposable non-degenerate solutions of the Yang-Baxter equation of multipermutation level 2. Next, applying Rosenbaum's theorem of subgroups of a semidirect product and isolating a triple: a subgroup of G, a subgroup of Zn2 and one group homomorphism, we obtain a~full description of each epimorphism which gives the desired solutions. Such a construction provides a tool how to find (and possibly enumerate) all indecomposable non-degenerate solutions of multipermutation level 2. We also argue that the automorphism group of the discussed solutions is regular.