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The Weil algebra and the Van Est isomorphism

Camilo Arias AbadMarius Crainic — 2011

Annales de l’institut Fourier

This paper belongs to a series of papers devoted to the study of the cohomology of classifying spaces. Generalizing the Weil algebra of a Lie algebra and Kalkman’s BRST model, here we introduce the Weil algebra W ( A ) associated to any Lie algebroid A . We then show that this Weil algebra is related to the Bott-Shulman complex (computing the cohomology of the classifying space) via a Van Est map and we prove a Van Est isomorphism theorem. As application, we generalize and find a simpler more conceptual...

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