A duality property for complex Lie algebroids

Abstract.

Interpreting Lie algebroid theory in terms of \({\cal D}\)-modules, we define a duality functor for a Lie algebroid as well as a direct image functor for a morphism of Lie algebroids. Generalizing the work of Schneiders (see also the work of Schapira-Schneiders) and making assumptions analog to his, we show that the duality functor and the direct image functor commute. As an application, we extend to Lie algebroids some duality properties already known for Lie algebras.