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Integrating Lie algebroids via stacks

Published online by Cambridge University Press:  13 January 2006

Hsian-Hua Tseng  and
Chenchang Zhu
Hsian-Hua Tseng
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, USAhhtseng@math.berkeley.edu
Chenchang Zhu
Affiliation:
Department Mathematik, ETH, Rämistrasse 101, 8092 Zürich, Switzerlandzhu@math.ethz.ch
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Abstract

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Lie algebroids cannot always be integrated into Lie groupoids. We introduce a new structure, ‘Weinstein groupoid’, which may be viewed as stacky groupoids. We use this structure to present a solution to the integration problem of Lie algebroids. It turns out that every Weinstein groupoid has a Lie algebroid and every Lie algebroid can be integrated into such a groupoid.

Keywords

Lie theoryLie algebroidsstacksgroupoids58H05 (primary)14A20 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 1 , January 2006 , pp. 251 - 270
Copyright
Foundation Compositio Mathematica 2006