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Sur la réductibilité de la variété des algèbres de Lie nilpotentes complexes

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Hakimjanov, Yu. B. and Ancochea Bermúdez, José María and Goze, Michel (1991) Sur la réductibilité de la variété des algèbres de Lie nilpotentes complexes. Comptes Rendus de l'Académie des Sciences. Série I. Mathématique, 313 (2). pp. 59-62. ISSN 0764-4442

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Abstract

Let Nn be the variety of nilpotent Lie algebra laws of a given complex vector space Cn. M. Vergne showed ["Variété des algèbres de Lie nilpotentes'', Thèse de 3ème cycle, Spéc. Math., Paris, 1966; BullSig(110) 1967:299; Bull. Soc. Math. France 98 (1970), 81–116; that Nn is irreducible for n≤6 and has at least two components for n=7 and n≥11. In this note, the authors prove the reducibility of Nn for n=8,9,10, thus answering affirmatively a question of Vergne. The last part of this work improves results of Vergne concerning some components of Nn, for n≥11.


Item Type:Article
Uncontrolled Keywords:reducibility; variety of complex nilpotent Lie algebras; perturbation; filiform Lie algebra; irreducible components
Subjects:Sciences > Mathematics > Algebra
ID Code:21123
Deposited On:29 Apr 2013 16:44
Last Modified:12 Dec 2018 15:13

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