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On certain families of naturally graded Lie algebras

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2002-05-08
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Elsevier Science
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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 ≡ 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 H2(g;C), it is shown that, with few exceptions, the isomorphism classes of these algebras are given by central extensions of Qn by Cp which preserve the nilindex and the natural graduation.
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