English

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.

Keywords

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

R2 v1 2026-06-21T11:06:55.693Z