Let $G$ and $G'$ be Compact connected Lie groups (which are not necessarily simply connected) with Lie algebra $\mathfrak{g}$ and $\mathfrak{h}$. Suppose that the two Lie algebras are isomorphic, under which conditions I can deduce that the Lie groups are also isomorphic?

Let $G$ and $G'$ be compact connected Lie groups (which are not necessarily simply connected) with Lie algebra $\mathfrak{g}$ and $\mathfrak{h}$. Suppose that the two Lie algebras are isomorphic, under which conditions I can deduce that the Lie groups are also isomorphic?

Let $G$ and $G'$ be Compact connected Lie groups (which are not necessarily simply connected)with Lie algebra $\mathfrak{g}$ and $\mathfrak{h}$. Suppose that the two Lie algebras are isomorphic, under which conditions I can deduce that the Lie groups are also isomorphic  ?

Let $G$ and $G'$ be Compact connected Lie groups (which are not necessarily simply connected) with Lie algebra $\mathfrak{g}$ and $\mathfrak{h}$. Suppose that the two Lie algebras are isomorphic, under which conditions I can deduce that the Lie groups are also isomorphic?