Nilpotent Lie algebras with 2-dimensional commutator ideals

AbstractWe classify all (finitely dimensional) nilpotent Lie k-algebras h with 2-dimensional commutator ideals h′, extending a known result to the case where h′ is non-central and k is an arbitrary field. It turns out that, while the structure of h depends on the field k if h′ is central, it is independent of k if h′ is non-central and is uniquely determined by the dimension of h. In the case where k is algebraically or real closed, we also list all nilpotent Lie k-algebras h with 2-dimensional central commutator ideals h′ and dimkh⩽11