Is there some relation between De Rham Cohomology group of Lie group as a manifold and group cohomology of Lie group?

At first glance, they are two different things. De Rham Cohomology group is defined by differential form on manifold. While group cohomology is used to classify the group extension.

My question:

1.For group cohomology $H^n_\sigma(G,A)$, we need group $G$, abelian group $A$ and $\sigma : G\rightarrow Aut(A)$. If I fixed $G$ is some Lie group, $A=\mathbb{R}$ and $\sigma$ as trivial homomorphism. Is there some relation between group cohomology $H^n_0(G,\mathbb{R})$ and De Rham cohomology $H^{n}_{dR}(G)$?



You must log in to answer this question.