
Journal of Lie Theory 18 (2008), No. 4, 811815 Copyright Heldermann Verlag 2008 A Converse to the Whitehead Theorem Pasha Zusmanovich Hlídarhjalli 62, Kópavogur 200, Iceland justpasha@gmail.com In this postscript to our earlier note [ J. Lie Theory 18 (2008) 295299] we show that finitedimensional Lie algebras over a field of characteristic zero such that their highdegree cohomology in any finitedimensional nontrivial irreducible module vanishes, are, essentially, direct sums of semisimple and nilpotent algebras. Keywords: Whitehead theorem, cohomology groups of Lie algebras. MSC: 17B56 [ Fulltextpdf (117 KB)] for subscribers only. 