# How can we prove a specific isomorphism between graded Lie algebra and graded universal enveloping algebra?

Let $$L$$ be a Lie algebra over field of characteristic different from $$2$$, and let $$L_n$$ be its descending central series. Therefore, we consider the associated graded Lie algebra $$gr^n L =frac{L_n}{L_{n+1}}$$. Moreover, let consider that the universal enveloping algebra $$U(L)$$ which is graded by the augmentation ideal denoted by $$I$$, that is, $$gr U(L)=oplus_{n geq 0} gr^{n} U(L)$$, where $$gr^{n}U(L)=I^n/I^{n+1}$$. How can we show that $$I^2/I^{3} cong L_2/L_3 otimes S_{2}(L/L_{2})$$, where $$S_{2}(L/L_{2})$$ is the symmetric algebra of $$gr^{2} L$$. Thank you for your time.