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Sur la variété des lois d'algèbres de Lie nilpotentes complexes

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Ancochea Bermúdez , José María and Goze, Michel (1989) Sur la variété des lois d'algèbres de Lie nilpotentes complexes. Rendiconti del Seminario della Facoltà di Scienze dell'Università di Cagliari , 58 (1-2). pp. 43-48. ISSN 0370-727X

Official URL: http://unica2.unica.it/~preside/index.php?id=22



Abstract

Let N i be the variety of laws of i -dimensional nilpotent complex Lie algebras, N ˜ i the quotient space of orbits under the canonical action of the full linear group and U i ⊂N i the open subset composed of filiform Lie algebras. M. Vergne determined U 7 and showed that N i is reducible for i=7 and i≥11 . In a previous paper the authors proved that U ˜ 8 and N ˜ 8 are unions of points and lines. In this note they study N 9 and choose in U 9 four continuous families with two parameters. One may ask whether each of these families generates a component of N 9 . However, it seems that the authors may give a positive answer to the problem of reducibility for N i , 8≤i≤10 .


Item Type:Article
Uncontrolled Keywords:nilpotent complex Lie algebra; filiform Lie algebras
Subjects:Sciences > Mathematics > Algebra
ID Code:21162
Deposited On:29 Apr 2013 17:53
Last Modified:12 Dec 2018 15:13

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