Lie algebroid

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In mathematics, a Lie algebroid <math>\mathcal{LA}</math> 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, where <math>T_{r}</math> denotes the restricted tangent space, as, <math> an: \mathcal{LA}\rightarrow T_{r}.</math>

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.