I'm studying the existence and the uniqueness of the universal enveloping algebra of a Lie algebra $\mathfrak{g}$ but i don't understand why $\mathfrak{U(g)}$ is generated by $i(\mathfrak{g})$, where $i$ is the following morphism: $$i: \mathfrak{g} \rightarrow \mathfrak{U}_{L}.$$
Is there anyone who can help me to understand?