The discourse begins with a definition of a Lie algebroid which is a vector bundle $p:A\to M$ over a manifold with an $R$-Lie algebra structure on the smooth section module and a bundle morphism $\gamma :A\to TM$ which induces a Lie algebra morphism on the smooth section modules. If $\gamma$ has constant rank, the Lie algebroid is called regular. (A monograph on the theory of Lie groupoids and Lie algebroids is published by K. Mackenzie [Lie groupoids and Lie algebroids in differential geometry (1987; Zbl 0683.53029)].) A principal $G$-bundle $(P,\pi ,M,G,·)$ gives rise to Lie algebroid $A\left(P\right)$. Since every vector bundle determines a $\text{GI}\left(n\right)$-principal bundle, it also determines a Lie algebroid. Many other examples illustrate the fact that Lie algebroids are a prevalent phenomenon. The author’s survey describes a theory of connections for regular Lie algebroids over a manifold equipped with a constant dimensional smooth distribution, and a!

EUDML-ID : urn:eudml:doc:221190
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@article{701508,
     title = {Characteristic classes of regular Lie algebroids -- a sketch},
     booktitle = {Proceedings of the Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {1993},
     pages = {[71]-94},
     mrnumber = {MR1246622},
     zbl = {0804.57016},
     url = {http://dml.mathdoc.fr/item/701508}
}

Kubarski, Jan. Characteristic classes of regular Lie algebroids – a sketch, dans Proceedings of the Winter School "Geometry and Physics", GDML_Books,  (1993), pp. [71]-94. http://gdmltest.u-ga.fr/item/701508/