Integrating Lie algebroids via stacks

2006/01/01 by Hsian‐Hua Tseng, Chenchang Zhu · 5 citations
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Double groupoid #Homotopy and Cohomology in Algebraic Topology #Lie algebra #Lie algebroid #Mathematics #Pure mathematics

paper · pdf · doi:10.1112/s0010437x05001752

openalex publication_date 2006/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

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.

Citations

• Topological and Smooth Stacks
• Integrating Lie algebroids via stacks and applications to Jacobi manifolds
• Integrability of Lie brackets
• Introduction to Foliations and Lie Groupoids
• The irreducibility of the space of curves of given genus

Cited by

• Higher U(1)-gerbe connections in geometric prequantization
• Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey
• Lie algebroid fibrations
• GROUPOIDS AND POISSON SIGMA MODELS WITH BOUNDARY
• Lie algebroid [wikipedia]