A converse to the Whitehead Theorem
Rings and Algebras
2009-06-06 v3 K-Theory and Homology
Abstract
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.
Cite
@article{arxiv.0808.0212,
title = {A converse to the Whitehead Theorem},
author = {Pasha Zusmanovich},
journal= {arXiv preprint arXiv:0808.0212},
year = {2009}
}
Comments
AMS-LaTeX; v3: fixed a typo