On action of outer derivations on nilpotent ideals of Lie algebras

Abstract

Action of outer derivations on nilpotent ideals of Lie algebras are considered.  It is shown that for a nilpotent ideal \(I\) of a Lie algebra \(L\) over a field \(F\) the ideal \(I+D(I)\) is nilpotent, provided that \(charF=0\) or \(I\)  nilpotent of nilpotency class less than \(p-1\), where \(p=char F\). In particular, the sum \(N(L)\) of all nilpotent ideals of a Lie algebra \(L\) is a characteristic ideal, if \(charF=0\) or \(N(L)\) is  nilpotent  of  class less than \(p-1\), where \(p=char F\).