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Journal of Lie Theory 18 (2008), No. 4, 811--815
Copyright Heldermann Verlag 2008

A Converse to the Whitehead Theorem

Pasha Zusmanovich
Hlídarhjalli 62, Kópavogur 200, Iceland

In this postscript to our earlier note [ J. Lie Theory 18 (2008) 295--299] we show that finite-dimensional Lie algebras over a field of characteristic zero such that their high-degree cohomology in any finite-dimensional non-trivial irreducible module vanishes, are, essentially, direct sums of semisimple and nilpotent algebras.

Keywords: Whitehead theorem, cohomology groups of Lie algebras.

MSC: 17B56

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