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Comptes Rendus Mathématique
Volume 337, n° 12
pages 757-759 (décembre 2003)
Doi : 10.1016/j.crma.2003.10.032
Received : 13 February 2003 ;  accepted : 21 October 2003
Une propriété topologique de l'ensemble des algèbres de Lie caractéristiquement nilpotentes
A topological property of the set of characteristically nilpotent Lie algebras

Jose María  Ancochea Bermúdez a ,  Rutwig  Campoamor-Stursberg b 1 ,  Michel  Goze b
aDepartamento de Geometría y Topología, Facultad CC. Matemáticas U.C.M, 28040 Madrid, Espagne 
bLaboratoire de mathématiques et applications, F.S.T., Université de Haute Alsace, 4, rue des Frères Lumière, 68093 Mulhouse cedex, France 

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Dans la variété des algèbres de Lie nilpotentes de dimension finie sur le corps des nombres complexes, l'ensemble des algèbres de Lie caractéristiquement nilpotentes n'est pas fermé. Nous montrons dans cette Note qu'il n'est pas ouvert non plus. Pour citer cet article : J.M. Ancochea Bermúdez et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).

Abstract

In the variety of finite dimensional nilpotent Lie algebras over the field of complex numbers, the set of characteristically nilpotent Lie algebras is not closed. In this Note we show that it is also not open. To cite this article: J.M. Ancochea Bermúdez et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).


1  Soutenu par une bourse de recherche de la Fondation Ramon Areces.




© 2003  Académie des sciences@@#104156@@

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