The Proceedings of the Winter School on Geometry and Physics, SRNI, January 1991, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II - numero 30 - anno 1993, 71-94.
publications
The notion of a Lie algebroid comes from J.Pradines (1967), and was invented in connection with the study of differential groupoids. This notion plays an analogous role as the Lie algebra of a Lie group. Observation concerning characteristic homomorphisms on the ground of principal bundles (such as the Chern-Weil homomorphism, the homomorphism of a flat or a partially flat principal bundle) show that they depend only on the Lie algebroids of these principal bundles. This enables us to bild a theory of characteristic classes for Lie algebroids and, next, to apply this technique to the investigation of some geometric structures defined on objects not being principal bundles but possessing Lie algebroids, such as transversally complete foliations, nonclosed Lie subgroups, Poisson manifolds or complete closed pseudogroups.
The part concerning primary characteristic classes generalizes results concerning transitive case given in [14]. Details can be found in next papers [29], [39].