I'm not an expert on Lie algebras and Lie groups, but I've learnt a very known theorem which states (someones call it Lie 3rd theorem):
"For every real finite dimensional Lie algebra $\mathfrak{g}$ exist one and only one connected and simply connected real Lie group $G$ such as $\mathfrak{g}=Lie(G)$".
Now, I'm asking if the complex version of the above theorem also holds, thus
"For every complex finite dimensional Lie algebra $\mathfrak{g}$ exist one and only one connected and simply connected complex Lie group $G$ such as $\mathfrak{g}=Lie(G)$".
Or, does exist a quite different, but essentially equivalent version of that theorem?
Thanks for the help,
Diego