I'd like to find a reference for the following result: $H^*(\mathfrak{u}(n); \mathbb{F}_p) \cong E_{\mathbb{F}_p}(x_1, x_3, ... , x_{2n-1})$, i.e., that the cohomology of the Lie algebra $\mathfrak{u}(n)$ - the Lie algebra corresponding to the Lie group $U(n)$ of $n \times n$ unitary matrices - is isomorphic to the cohomology of the exterior algebra over $\mathbb{F}_p$ on odd degree generators.
I believe the desired isomorphism is obtained by either the Serre spectral sequence or Hochschild-Serre spectral sequence calculations.
Thanks in advance!
~Mo