# Article

 Title: Pontryagin algebra of a transitive Lie algebroid (English) Author: Kubarski, Jan Language: English Journal: Proceedings of the Winter School "Geometry and Physics" Volume: Issue: 1989 Year: Pages: [117]-126 . Category: math . Summary: [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: $h\sp p: (Vg\sp*)\sb I\to {\cal H}(M)$. (English) MSC: 55R25 MSC: 55R40 MSC: 57R20 MSC: 57R22 MSC: 57T10 MSC: 58H05 idZBL: Zbl 0711.55010 idMR: MR1061794 . Date available: 2009-07-13T21:24:52Z Last updated: 2012-09-18 Stable URL: http://hdl.handle.net/10338.dmlcz/701467 .

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