A NOTE ON DERIVATIONS OF LIE ALGEBRAS

Publisher： Cambridge University Press

E-ISSN： 1755-1633|84|3|444-446

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.84, Iss.3, 2011-07, pp. : 444-446

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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 \[ L^n\subseteq \sum _{d\in D}d(L), \] 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.

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