
Journal of Lie Theory 18 (2008), No. 2, 295299 Copyright Heldermann Verlag 2008 A Converse to the Second Whitehead Lemma Pasha Zusmanovich Hlídarhjalli 62, Kópavogur 200, Iceland justpasha@gmail.com In this paper we state and prove the following version of a converse to the Second Whitehead Lemma: A finitedimensional Lie algebra over a field of characteristic zero with vanishing second cohomology in any finitedimensional module must be one of the following: (i) a onedimensional algebra; (ii) a semisimple algebra; (iii) the direct sum of a semisimple algebra and a onedimensional algebra. Keywords: Second Whitehead Lemma. MSC: 17B56 [ Fulltextpdf (123 KB)] for subscribers only. 