| Title | The Weil algebra and the Van Est isomorphism |
|---|---|
| Published in | Annales de l'Institut Fourier, Vol. 61, p.927-970. ISSN 0373-0956. |
| Author | Arias Abad, C.; Crainic, M. |
| Date | 2011 |
| Language | English |
| Type | article |
| Publisher | Association des Annales de l'Institut Fourier |
| 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 et.al. 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. |
| Publication | http://igitur-archive.library.uu.nl/math/2012-0308-200338/UU... |
| Persistent Identifier | URN:NBN:NL:UI:10-1874-234172 |
| Metadata | XML |
| Repository | Utrecht University |
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