A Lie groupoid over B is a groupoid G for which G and B are differentiable manifolds and α, β and multiplication are differentiable maps. Furthermore, the derivatives of α and β are required to have maximal matrix rank everywhere. Here, α and β are maps from G onto B.

groupoid | Lie algebroid | nilpotent Lie group | semisimple Lie group | solvable Lie group

Marius Sophus Lie