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A NOTE ON DERIVATIONS OF LIE ALGEBRAS
Published online by Cambridge University Press: 21 July 2011
Abstract
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.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 84 , Issue 3 , December 2011 , pp. 444 - 446
- Copyright
- Copyright © Australian Mathematical Publishing Association Inc. 2011
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