Exponential map (Lie theory)

In the theory of Lie groups, the exponential map is a map from the Lie algebra g {\displaystyle {\mathfrak {g}}} of a Lie group G {\displaystyle G} to the group, which allows one to recapture the local group structure from the Lie algebra. The existence of the exponential map is one of the primary reasons that Lie algebras are a useful tool for studying Lie groups.