lie algebroid

In mathematics, a Lie algebroid

\mathcal{LA}

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

an: \mathcal{LA}\rightarrow T_{r}

(

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.

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