On certain families of naturally graded Lie algebras

Abstract

In this work large families of naturally graded nilpotent Lie algebras in arbitrary dimension and characteristic sequence ( n, q,1) with n≡1( mod 2) satisfying the centralizer property are given. This centralizer property constitutes a generalization, for any nilpotent algebra, of the structural properties characterizing the Lie algebra Q n . By considering certain cohomological classes of the space H 2( g, C) , it is shown that, with few exceptions, the isomorphism classes of these algebras are given by central extensions of Q n by C p which preserve the nilindex and the natural graduation.