I am revising for my Lie Groups exam and am stuck on the following question.
Find all Lie Group homomorphisms
a) $ \ F : \mathbb{R} \longrightarrow S^1 \ $ (Hint: Consider the corresponding homomorphisms of Lie algebras $F_{\ast}$)
b) $ \ F : S^1 \longrightarrow \mathbb{R} $
where $S^1$ is the unit circle.
I don't really know where to begin with this so any help would be very much appreciated?