Communications in algebra vol:31 issue:12 pages:5847-5874
We construct Z-gradings for all 3-generated 3-step nilpotent and 2-generated 4-step nilpotent Lie algebras. This shows that all 3-generated 4-step nilpotent and 2-generated 5-step nilpotent Lie algebras have a complete affine structure. We also obtain a lower bound on the number of generators of a c-step nilpotent Lie algebra with singular derivation algebra. Examples indicate this bound is sharp.