Within the book *An introduction to homological algebra* by Weibel, I am trying to prove the following isomorphism, but I am not sure this is true. But I really want to know how to prove or disprove it.

**Notation:**
Let $\mathfrak{g}$ be a finite dimensional Lie algebra over a field.
Let $\text{H}^i_{\text{Lie}}(\mathfrak{g},A)$ be the i-th cohomology group of $\mathfrak{g} $ with the coefficients in the $\mathfrak{g}$-module $A$.

**Page 226:**
Let $M,N$ be $\mathfrak{g}$-modules. Then we have the following natural isomorphism of $\delta$ functors:

$$ \text{Ext}^\ast_{U \mathfrak{g}}(M,N) \cong \text{H}^\ast_{\text{Lie}}(\mathfrak{g}, \text{Hom}_{k}(M,N)) $$

where $\ast$ is a non-negative integer.

Thanks very much!