Reduction of Poisson–Nijenhuis Lie algebroids to symplectic-Nijenhuis Lie algebroids with a nondegenerate Nijenhuis tensor

DOI10.1088/1751-8113/44/42/425206zbMATH Open1254.53109arXiv1105.4858OpenAlexW3106261133MaRDI QIDQ3096516

Antonio De Nicola, Edith Padrón, Juan Carlos Marrero

Publication date: 11 November 2011

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Abstract: We show how to reduce, under certain regularities conditions, a Poisson-Nijenhuis Lie algebroid to a symplectic-Nijenhuis Lie algebroid with nondegenerate Nijenhuis tensor. We generalize the work done by Magri and Morosi for the reduction of Poisson-Nijenhuis manifolds. The choice of the more general framework of Lie algebroids is motivated by the geometrical study of some reduced bi-Hamiltonian systems. An explicit example of reduction of a Poisson-Nijenhuis Lie algebroid is also provided.

Full work available at URL: https://arxiv.org/abs/1105.4858

zbMATH Keywords

reduction Lie algebroids bi-Hamiltonian systems nondegenerate Nijenhuis tensors Poisson-Nijenhuis Lie algebroids symplectic-Nijenhuis Lie algebroids

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) Symplectic manifolds (general theory) (53D05) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Poisson manifolds; Poisson groupoids and algebroids (53D17) Lie bialgebras; Lie coalgebras (17B62)