Wolfgang Alexander Moens
"A characterisation of nilpotent Lie algebras by their (generalised) derivations."
Jacobson proved that if a Lie algebra admits an invertible derivation, it must be
nilpotent. He also suspected, though incorrectly, that the converse might be true: that every
nilpotent Lie algebra has an invertible derivation. We prove that a Lie algebra is nilpotent
if and only if it admits an invertible generalised-derivation. The proofs are elementary in nature
and are based on well-known techniques (in the field of Lie algebras).