Naturally graded quasi-filiform Lie algebras

We present the classification of one type of graded nilpotent Lie algebras. We start from the gradation related to the filtration which is produced in a natural way by the descending central sequence in a Lie algebra. These gradations were studied by Vergne [Bull. Soc. Math. France 98 (1970) 81–116] and her classification of the graded filiform Lie algebras is here extended to other algebras with a high nilindex. We also show how symbolic calculus can be useful in order to obtain results in a similar classification problem.