In this note, we will prove that a finite dimensional Lie algebra L of
characteristic zero, admitting an abelian algebra of derivations Dβ€Der(L)
with the property LnβdβDββd(L) for some nβ₯1, is
necessarily solvable. As a result, if L has a derivation d:LβL, such
that Lnβd(L), for some nβ₯1, then L is solvable.Comment: 4 page