TITLE: What is the connection between Frechet Lie groups and Lie algebras?
QUESTION [5 upvotes]: An ordinary Lie group has a differentiable manifold structure, i.e. it is locally isomorphic to a finite-dimensional Euclidean space.  A Frechet Lie group, on the other hand, has a Frechet manifold structure, i.e. it is locally isomorphic to an infinite-dimensional Frechet space.
My question is, what is the connection between Frechet Lie groups and Lie algebras?  Wikipedia says this:

Some of the relations between Lie algebras and Lie groups remain valid in this setting.

But which ones remain valid and which ones don’t?

REPLY [2 votes]: Karl Hermann Neeb has lecture notes from a course on infinite-dimensional Lie theory given at a summer school in Monastir. They can be found for example here.