Geodesic
On the functorial prolongations of principal bundles
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 4, pp. 719-731.

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We describe the fundamental properties of the infinitesimal actions related with functorial prolongations of principal and associated bundles with respect to fiber product preserving bundle functors. Our approach is essentially based on the Weil algebra technique and an original concept of weak principal bundle.
Classification : 58A20, 58A32, 58H05
Keywords: fiber product preserving bundle functor; weak principal bundle; Lie algebroid; functorial prolongation; Weil algebra 
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Kolář, Ivan; Cabras, Antonella. On the functorial prolongations of principal bundles. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 4, pp. 719-731. http://geodesic.mathdoc.fr/item/CMUC_2006__47_4_a15/