Cohomology groups of semisimple Lie algebras and Lie groups over $\mathbb{R}$

Question

As the title suggests I am looking for a reference for the cohomology groups of semisimple Lie algebras over $\mathbb{R}$ with coefficients in $\mathbb{R}$ and for the de Rham cohomology groups of the semisimple, simply connected Lie groups, associated to them.

Since there is a classification for semisimple Lie algebras and therefore also for semisimple, simply connected Lie groups, I suspect such a reference should exist somewhere.

Also for the compact semisimple case those two are isomorphic not only to each other but also to the cohomology groups of the associated complex semisimple Lie algebra, if I am not mistaken, so that reduces this case a bit.

However, I am also interested in the non-compact cases.

Thanks in advance for any suggestions/corrections!

Answer 1

Look into Lie Groups Beyond an Introduction by Knapp, or Differential Geometry, Lie Groups, and Symmetric Spaces by Helgason.

Answer 2

A classical reference is the paper by C. Chevalley and S. Eilenberg, Cohomology Theory of Lie Groups and Lie Algebras. By the Whitehead lemmas we have $H^1(L,\Bbb R)=H^2(L,\Bbb R)=0$. For the third cohomology group, however, this is no longer true.