Let $ G$ be an algebraic group. We can try to reconstruct $ G$ from its lie algebra $ \mathfrak{g}$ , but the best we get in general is a formal group scheme $ \operatorname{Spf}(U(\mathfrak{g})^*)$ , where $ U(\mathfrak{g})$ is the universal enveloping algebra of $ \mathfrak{g}$ .

However, I have heard that certain conditions provide for a full reconstruction of $ G$ . Namely, if $ G$ is connected and simply connected, then there is an isomorphism $ \mathcal{O}(G) \rightarrow U(\mathfrak{g})^{\circ}$ , where $ U(\mathfrak{g})^{\circ}$ is the Hopf dual of $ U(\mathfrak{g})$ .

I can’t seem to find a reference for this. Could someone please provide one?