On certain families of naturally graded Lie algebras

Ancochea, Jose Maria; Campoamor, Otto Rutwig

On certain families of naturally graded Lie algebras

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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 $H^{2}(\frak{g},\mathbb{C})$, 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