Symmetric algebra and complex polynomial on Lie algebra

Question

Let $G$ a Lie group and $\mathfrak{G}$ its Lie algebra. How can I identify the symmetric algebra on $\mathfrak{G}$ ($S(\mathfrak{G})$) with the algebra of complex polynomials on $\mathfrak{G}$, that I denote with $\mathbb{C}[\mathfrak{G}]$'