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Mar 4, 2012 at 17:52 comment added darij grinberg Okay. This is exactly the reverse of Cartier's argument, as he uses the invariant-theoretical statement to prove the cohomology of $U_n$ rather than the other way round. (He is doing this for the sake of historical authenticity, I assume - there were no Leray spectral sequences at the time when the cohomology of Lie groups was first computed.) But +1 for a nice application of geometry in algebra.
Mar 4, 2012 at 17:02 history answered Vladimir Dotsenko CC BY-SA 3.0