The Weil algebra and the Van Est isomorphism (2011) Open access

Title The Weil algebra and the Van Est isomorphism
Published in Annales de l'Institut Fourier, Vol. 61, No. 3, p.927-. ISSN 0373-0956.
Author Arias Abad, C; Crainic, M.
Date 2011
Language English
Type Article
Abstract This paper belongs to a series 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-Stasheff 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 proof of the main result of Bursztyn on the reconstructions of multiplicative forms and of a result of Weinstein-Xu and Crainic on the reconstruction of connection 1-forms. This reveals the relevance of the Weil algebra and Van Est maps to the integration and the pre-quantization of Poisson (and Dirac) manifolds.
Persistent Identifier URN:NBN:NL:UI:10-1874-234172
Metadata XML
Repository Utrecht University

Go to page top
Go back to contents
Go back to site navigation