Let $L$ be a Lie algebra over $\mathbb{C}$. Assume $L$ satisfies PBW theorem. We can associate two Lie algebras with $L$:
1) $U(L):$ the universal enveloping algebra. Here the Lie bracket is defined by $[x,y]=x*y-y*x$ where $*$ is the product induced from tensor product.
2)$S(L):$ the symmetric algebra. Here the Lie bracket is defined by extending the Leibniz rule $[xy,z]=x[y,z]+[x,z]y.$
Q) Are theses two Lie algebras isomorphic as Lie algebras.