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

We show how to reduce, under certain regularity conditions, a Poisson-Nijenhuis Lie algebroid to a symplectic-Nijenhuis Lie algebroid with a 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 the reduction of a Poisson-Nijenhuis Lie algebroid is also provided.