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Integrating Lie algebroids via stacks and applications to Jacobi manifolds

Chenchang Zhu
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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. Furthermore, we apply this general result to Jacobi manifolds and construct contact groupoids for Jacobi manifolds. There are further applications in prequantization and integrability of Poisson bivectors.

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Chenchang Zhu. 2025-04-14. Integrating Lie algebroids via stacks and applications to Jacobi manifolds. https://arxiv.org/abs/math/0505158

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