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arXiv · 2410.08671

Poisson quasi-Nijenhuis manifolds, closed Toda lattices, and generalized recursion relations

Eber Chuño Vizarreta·Gregorio Falqui·Igor Mencattini·Marco Pedroni
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Abstract

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.

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Eber Chuño Vizarreta, Gregorio Falqui, Igor Mencattini, Marco Pedroni. 2024-10-11. Poisson quasi-Nijenhuis manifolds, closed Toda lattices, and generalized recursion relations. https://arxiv.org/abs/2410.08671

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