On certain families of naturally graded Lie algebras

Jose Maria Ancochea; Otto Rutwig Campoamor

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On certain families of naturally graded Lie algebras

Jose Maria Ancochea·Otto Rutwig Campoamor

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

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Jose Maria Ancochea, Otto Rutwig Campoamor. 2000-10-23. On certain families of naturally graded Lie algebras. https://arxiv.org/abs/math/0010216

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