Quasi-filiform Lie algebras of maximum length revisited

Abstract We revisit the problem of classification of quasi-filiform Lie algebras of maximum length. The lists found in the literature are either incomplete or non-explicit. En route we touch upon the classification of graded filiform Lie algebras generated by two elements of degree one and three, respectively, and, as a byproduct, obtain a classification of N -graded infinite-dimensional Lie algebras with one-dimensional homogeneous components of coclass two.