Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Journal of Lie Theory 18 (2008), No. 2, 295--299
Copyright Heldermann Verlag 2008

A Converse to the Second Whitehead Lemma

Pasha Zusmanovich
Hlídarhjalli 62, Kópavogur 200, Iceland

In this paper we state and prove the following version of a converse to the Second Whitehead Lemma: A finite-dimensional Lie algebra over a field of characteristic zero with vanishing second cohomology in any finite-dimensional module must be one of the following: (i) a one-dimensional algebra; (ii) a semisimple algebra; (iii) the direct sum of a semisimple algebra and a one-dimensional algebra.

Keywords: Second Whitehead Lemma.

MSC: 17B56

[ Fulltext-pdf  (123  KB)] for subscribers only.