Lie algebroid

In mathematics, a Lie algebroid can be thought of as a restricted Lie module that has both a Lie bracket and a Lie algebra morphism, known as an anchor map , given as

(

with T_r denoting the restricted tangent space), associated to it.

The standard example of a Lie algebroid is the identity map corresponding to the tangent space of a Lie groupoid. It is a generalization of a Lie algebra for groupoids.