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Evgeny Shinder
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Cohomology rings of GL_n(C), SL_n(C)

Can anyone provide me with the reference for the following fact (idea of the proof will be appreciated too):

Cohomology ring with $\mathbb Q$-coefficients of a group $G$ (I don't know precisely what the assumptions are: reductive complex algebraic group or maybe complex Lie group G with some restrictions. The cases I'm interested in are $GL_n(\mathbb C)$ and $SL_n(\mathbb C)$) is the exterior algebra on the generators of odd degrees, with the number of generators equal to the rank of $G$.

This fact is attributed to H.Hopf, but I wasn't able to find a reference.

Thanks.

Evgeny Shinder
  • 1.8k
  • 14
  • 30