Dimensionally nilpotent Lie algebras (Q1105681)

An \(n\)-dimensional Lie algebra \(L\) is dimensionally nilpotent if it has a nilpotent derivation \(\Delta\) with \(\Delta^{n-1}\ne 0\). The first of the two theorems in this short paper says that a dimensionally nilpotent Lie algebra over a field of characteristic 0 must either be solvable or be simple of dimension 3. The second theorem pursues the solvable case and presents results regarding a maximal nilpotent ideal in \(L\).