  Recently Kontsevich solved the classification problem for deformation
quantizations of all Poisson structures on a manifold. In this paper we study
those Poisson structures for which the explicit methods of Fedosov can be
applied, namely the Poisson structures coming from symplectic Lie algebroids,
as well as holomorphic symplectic structures. For deformations of these
structures we prove the classification theorems and a general a general index
theorem.
