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

Journal of Physics A Mathematical General
 Pub Date:
 October 2011
 DOI:
 10.1088/17518113/44/42/425206
 arXiv:
 arXiv:1105.4858
 Bibcode:
 2011JPhA...44P5206D
 Keywords:

 Mathematics  Differential Geometry;
 Mathematical Physics;
 Mathematics  Symplectic Geometry;
 53D17 (Primary) 17B62;
 17B66;
 37J05;
 37J35;
 37K10 (Secondary)
 EPrint:
 35 pages, final version to appear in J. Phys. A: Math. Theor