Lie's third theorem

Overview

Sophus Lie proved 3 theorems relating Lie groups and their Lie algebras. This is often seen as the “most important” one and gives that the functor

is essentially surjective.

Lie’s third theorem

For any finite-dimensional real Lie algebra , there exists a conected, simply-connected Lie group that is unique (up to isomorphism) such that its Lie algebra