Lie algebroid

In mathematics, Lie algebroids serve the same role in the theory of Lie groupoids that Lie algebras serve in the theory of Lie groups: reducing global problems to infinitesimal ones.Just as a Lie groupoid can be thought of as a 'Lie group with many objects', a Lie algebroid is like a 'Lie algebra with many objects'.To describe the construction let us fix some notation. G is the space of morphisms of the Lie groupoid, M the space of objects, e : M → G {displaystyle e:M o G}   the units and t : G → M {displaystyle t:G o M}   the target map.