# Lie algebras of infinite dimensional Lie groups

I have to work with Lie algebras of some infinite dimensional 'Lie groups' (e.g. $$\Omega SL_2(\mathbb{C})$$) but i'm not sure on how to approach infinite dimensional groups, for loop group it is not so obvious what should be considered a neighborhood of the identity. I don't want to see the whole solution, maybe just some hints, but much more i would appreciate an explanation (or some reference) of how one should view local structure of such groups.

"As in finite dimensions, the tangent space $$L(G) := T_1(G)$$ at the identity element of a Lie group $$G$$ can be made a topological Lie algebra via the identification with the Lie algebra of left invariant vector fields on $$G$$."