[For the entire collection see Zbl 0699.00032.] It was previously known that for every principal fibre bundle P there is some corresponding transitive Lie algebroid A(P) - a vector bundle equipped with some structure like the structure of a Lie algebra in the module of sections. The author of this article shows that the Chern-Weil homomorphism of P is a notion of the Lie algebroid of P, i.e. knowing only A(P) of P one can uniquely reproduce the ring of invariant polynomials and the Chern-Weil homomorphism: .
@article{701467,
title = {Pontryagin algebra of a transitive Lie algebroid},
booktitle = {Proceedings of the Winter School "Geometry and Physics"},
series = {GDML\_Books},
publisher = {Circolo Matematico di Palermo},
address = {Palermo},
year = {1990},
pages = {[117]-126},
mrnumber = {MR1061794},
zbl = {0711.55010},
url = {http://dml.mathdoc.fr/item/701467}
}
Kubarski, Jan. Pontryagin algebra of a transitive Lie algebroid, dans Proceedings of the Winter School "Geometry and Physics", GDML_Books, (1990), pp. [117]-126. http://gdmltest.u-ga.fr/item/701467/