Integrating Lie algebroids via stacks
Abstract
Lie algebroids can not always be integrated into Lie groupoids. We introduce a new object--``Weinstein groupoid'', which is a differentiable stack with groupoid-like axioms. With it, we have solved 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 a Weinstein groupoid.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- April 2004
- DOI:
- 10.48550/arXiv.math/0405003
- arXiv:
- arXiv:math/0405003
- Bibcode:
- 2004math......5003T
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematics - Algebraic Geometry
- E-Print:
- a proof improved