On certain families of naturally graded Lie algebras

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 Qn. By considering certain cohomological classes of the space image, it is shown that, with few exceptions, the isomorphism classes of these algebras are given by central extensions of Qn by image which preserve the nilindex and the natural graduation.