A converse to the Whitehead Theorem
classification
🧮 math.RA
math.KT
keywords
algebrasfinite-dimensionalcharacteristiccohomologyconversedirectessentiallyfield
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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.
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