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Dec 13, 2009 at 20:08 vote accept Theo Johnson-Freyd
Dec 13, 2009 at 19:56 comment added Pete L. Clark I agree with MSA. Look in Serre's Lie Algebras and Lie Groups: he proves Lie III for Lie algebras over any nondiscrete, locally compact field. Part I of the book is on Lie algebras, but it is generally agreed that it covers only the more formal aspects and not the fine structure theory of Lie algebras: e.g. no roots or weights. (His book Complex Semisimple Lie Algebras has more of this sort of thing.) Accordingly, I am no expert but I would say that Lie III is in fact not that difficult compared to some other big theorems in basic Lie theory.
Dec 13, 2009 at 19:46 history edited Mariano Suárez-Álvarez CC BY-SA 2.5
ALways give a reference... Serre has too many books
Dec 13, 2009 at 19:41 history answered Mariano Suárez-Álvarez CC BY-SA 2.5