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A duality property for complex Lie algebroids. (English) Zbl 0933.32015
Interpreting Lie algebroid theory in terms of $${\mathcal D}$$-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.

##### MSC:
 32C38 Sheaves of differential operators and their modules, $$D$$-modules 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties 58H05 Pseudogroups and differentiable groupoids
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