In this note, we will prove that a finite-dimensional Lie algebra L over a field of characteristic zero, admitting an abelian algebra of derivations D≤Der(L), with the property Ln ⊆ ∑d∈D d(L), for some n>1, is necessarily solvable. As a result, we show that if L has a derivation d:L→L such that Ln⊆d(L), for some n>1, then L is solvable.
|Number of pages||3|
|Journal||Bulletin of the Australian Mathematical Society|
|Publication status||Published - Dec 2011|
- Lie algebras
- compact Lie groups
- solvable Lie algebras
ASJC Scopus subject areas