Poincaré duality for transitive unimodular invariantly oriented Lie algebroids

Fubiniʹs formula for an oriented bundle suggests a definition of the integration of forms of maximal degree in a transitive Lie algebroid A (using the fibre integral ∫A in A, defined and investigated by the author in his previous paper). In the case of a unimodular and invariantly oriented transitive Lie algebroid, this integral enables us to define the Poincaré scalar product. The purpose of this paper is to investigate the fundamental properties of this product.