Lie algebroid

Summary

A Lie algebroid is a vector bundle over a manifold whose sections carry a Lie bracket. It comes with a bundle map to the tangent bundle, the anchor, that turns sections into vector fields. It contains both the tangent bundle of a manifold and a finite-dimensional Lie algebra as extreme cases. Lie algebroids are the infinitesimal objects of Lie groupoids, as Lie algebras are the infinitesimal objects of Lie groups. They appear in Poisson geometry, foliation theory and the study of group actions on manifolds.