Poisson quasi-Nijenhuis manifolds, closed Toda lattices, and generalized recursion relations
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918089740779520 |
|---|---|
| author | Vizarreta, Eber Chuño Falqui, Gregorio Mencattini, Igor Pedroni, Marco |
| author_facet | Vizarreta, Eber Chuño Falqui, Gregorio Mencattini, Igor Pedroni, Marco |
| contents | We present two involutivity theorems in the context of Poisson quasi-Nijenhuis %(PqN) manifolds. The second one stems from recursion relations that generalize the so called Lenard-Magri relations on a bi-Hamiltonian manifold. We apply these results to the closed (or periodic) Toda lattices of type $A_n^{(1)}$, $C_n^{(1)}$, $A_{2n}^{(2)}$ and, for the ones of type $A^{(1)}_n$, we show how this geometrical setting relates to their bi-Hamiltonian representation and to their recursion relations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08671 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Poisson quasi-Nijenhuis manifolds, closed Toda lattices, and generalized recursion relations Vizarreta, Eber Chuño Falqui, Gregorio Mencattini, Igor Pedroni, Marco Mathematical Physics 37J35, 53D17, 70H06 We present two involutivity theorems in the context of Poisson quasi-Nijenhuis %(PqN) manifolds. The second one stems from recursion relations that generalize the so called Lenard-Magri relations on a bi-Hamiltonian manifold. We apply these results to the closed (or periodic) Toda lattices of type $A_n^{(1)}$, $C_n^{(1)}$, $A_{2n}^{(2)}$ and, for the ones of type $A^{(1)}_n$, we show how this geometrical setting relates to their bi-Hamiltonian representation and to their recursion relations. |
| title | Poisson quasi-Nijenhuis manifolds, closed Toda lattices, and generalized recursion relations |
| topic | Mathematical Physics 37J35, 53D17, 70H06 |
| url | https://arxiv.org/abs/2410.08671 |