On local integration of Lie brackets

Abstract

We give a direct, explicit and self-contained construction of a local Lie groupoid integrating a given Lie algebroid which only depends on the choice of a spray vector field lifting the underlying anchor map. This construction leads to a complete account of local Lie theory and, in particular, to a finite-dimensional proof of the fact that the category of germs of local Lie groupoids is equivalent to that of Lie algebroids.

26 pages; the previous version (v1) was split into two papers, this is the first one and the second one will appear separatedly

Cited by in corpus (10)

• Holomorphic Jacobi Manifolds and Holomorphic Contact Groupoids
• Van Est differentiation and integration
• Brane quantization of toric Poisson varieties
• Contact Dual Pairs
• Generating functions for local symplectic groupoids and non-perturbative semiclassical quantization
• Local formulas for multiplicative forms
• Poisson double structures
• Dimensional reduction of Courant sigma models and Lie theory of Poisson groupoids
• Local and global integrability of Lie brackets
• Involution algebroids: a generalisation of Lie algebroids for tangent categories