A Converse to the Whitehead Theorem
Copyright policy )A Converse to the Whitehead Theorem
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.
AMS-LaTeX; v3: fixed a typo
Lie algebra cohomology, Rings and Algebras (math.RA), Mathematics - K-Theory and Homology, FOS: Mathematics, Whitehead theorem, K-Theory and Homology (math.KT), Mathematics - Rings and Algebras, Cohomology of Lie (super)algebras, Whitehead lemma, 17B56
Lie algebra cohomology, Rings and Algebras (math.RA), Mathematics - K-Theory and Homology, FOS: Mathematics, Whitehead theorem, K-Theory and Homology (math.KT), Mathematics - Rings and Algebras, Cohomology of Lie (super)algebras, Whitehead lemma, 17B56
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