Salvato in:
| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2508.17981 |
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Sommario:
- 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 \emph{the universal} one. On the other hand we prove that there is much simpler description. At first, on the product of a group $Z_n^2$ 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 $Z_n^2$ 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.