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 odd, satisfying the centralizer property, are given. This condtion constitutes a generalization, for a nilpotent Lie agebra, of the structural properties charactrizing the Lie algebra $Q_n$. By considering certain cohomological classes of the space $H^2(\mathfrak{g},\mathbb{C})$, it is shown that, with few exceptions, the isomorphism classses of these algebras are given by central extensions of $Q_n$ by ${\mathbb{C}}^p$ which preserve the nilindex and the natural graduation.

30 pages, 2 tables