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A NOTE ON DERIVATIONS OF LIE ALGEBRAS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 84 / Issue 3 / December 2011
- Published online by Cambridge University Press:
- 21 July 2011, pp. 444-446
- Print publication:
- December 2011
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- Article
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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
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.
