We prove that any set-theoretic solution of the Yang–Baxter equation associated with a dual weak brace is a strong semilattice of non-degenerate bijective solutions. This fact makes use of the description of any dual weak brace S we provide in terms of strong semilattice Y of skew braces Bα, with α∈Y. Additionally, we describe the ideals of S and study its nilpotency by correlating it to that of each skew brace Bα.
Solutions of the Yang–Baxter Equation and Strong Semilattices of Skew Braces
Catino F.;Mazzotta M.;Stefanelli P.
2024-01-01
Abstract
We prove that any set-theoretic solution of the Yang–Baxter equation associated with a dual weak brace is a strong semilattice of non-degenerate bijective solutions. This fact makes use of the description of any dual weak brace S we provide in terms of strong semilattice Y of skew braces Bα, with α∈Y. Additionally, we describe the ideals of S and study its nilpotency by correlating it to that of each skew brace Bα.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
s00009-024-02611-6.pdf
accesso aperto
Descrizione: Solutions of the Yang–Baxter Equation and Strong Semilattices of Skew Braces
Tipologia:
Versione editoriale
Licenza:
Creative commons
Dimensione
460.46 kB
Formato
Adobe PDF
|
460.46 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
