Journal of Lie Theory 18 (2008), No. 2, 295--299
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 finite-dimensional Lie algebra over a field of characteristic zero with vanishing second cohomology in any finite-dimensional module must be one of the following: (i) a one-dimensional algebra; (ii) a semisimple algebra; (iii) the direct sum of a semisimple algebra and a one-dimensional algebra.
Keywords: Second Whitehead Lemma.
MSC: 17B56
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