Integrating Lie algebroids via stacks and applications to Jacobi manifolds
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2005
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| _version_ | 1866910910956699648 |
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| author | Zhu, Chenchang |
| author_facet | Zhu, Chenchang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0505158 |
| institution | arXiv |
| publishDate | 2005 |
| record_format | arxiv |
| spellingShingle | Integrating Lie algebroids via stacks and applications to Jacobi manifolds Zhu, Chenchang Differential Geometry Symplectic Geometry 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. |
| title | Integrating Lie algebroids via stacks and applications to Jacobi manifolds |
| topic | Differential Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/math/0505158 |