Return to Revisions

Cohomology does not change under field extensions, so just extend everything to the algebraic closure to prove your result in char 0 in general. Of course, field extensions do not preserve irreducibility, but they preserve semi-simplicity, and preserve the property of having a trivial factor in the decomposition into irreducibles. (That works if you allow to use the complete reducibility in the algebraically closed case, not if you want to prove it using Whitehead's lemma.)