Publication: Sur les composantes de la variété des algèbres de Lie nilpotentes
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Publication Date
1992
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Elsevier
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Abstract
The scheme of the Lie algebras of dimension n is reducible for n≥2 and the number of its components is bounded asymptotically by exp(n/4) . The same problem is studied by the authors for the subvariety N n of the nilpotent Lie algebras of dimension n . For n≥7 , N n is reducible and it is proved in this paper that there exists at least one component which does not contain filiform laws. Then the authors give an asymptotic estimation, equal to n/74 , for the number of the components of N n .