Integrating Lie algebroids via stacks and applications to Jacobi manifolds
Differential Geometry
2025-04-15 v2 Symplectic Geometry
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.
Keywords
Cite
@article{arxiv.math/0505158,
title = {Integrating Lie algebroids via stacks and applications to Jacobi manifolds},
author = {Chenchang Zhu},
journal= {arXiv preprint arXiv:math/0505158},
year = {2025}
}
Comments
Ph. D. thesis, 2004, U.C. Berkeley; references edited; typos corrected