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[For the entire collection see Zbl 0699.00032.] \par 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 $(Vg\sp*)\sb I$ and the Chern-Weil homomorphism: $h\sp p: (Vg\sp*)\sb I\to {\cal H}(M)$.
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