Quasi-filiform Lie algebras of great length (Q947485)

This is another incremental step in ongoing efforts to classify what is amenable to classification in the realm of nilpotent Lie algebras, i.e. filiform and close to them algebras. An \(n\)-dimensional Lie algebra is called quasi-filiform if its lower central series terminates exactly at the \((n-2)\)th step. The length of such algebra is the maximum of lengths of its \(\mathbb N\)-gradations. Here, graded quasi-filiform Lie algebras of finite dimension \(n \geq 15\) and length \(n-1\), are classified. There are \(22\) types of such algebras, some of then constitute parametric families. The paper consists, essentially, of long and cumbersome computations performed with the aid of Mathematica.