Whitehead's lemma (Lie algebras)
In algebra, Whitehead's lemma on a Lie algebra representation (named after J. H. C. Whitehead) is an important step toward the proof of Weyl's theorem on complete reducibility. Let be a semisimple Lie algebra over a field of characteristic zero, V a finite-dimensional module over it and a linear map such that . The lemma states that there exists a vector v in V such that for all x.
- Jacobson, Nathan, Lie algebras, Republication of the 1962 original. Dover Publications, Inc., New York, 1979. ISBN 0-486-63832-4