Hakimjanov, Yu. B.Ancochea Bermúdez, José MaríaGoze, Michel2023-06-202023-06-2019910764-4442https://hdl.handle.net/20.500.14352/58437Let 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.frajournal articlehttp://gallica.bnf.fr/ark:/12148/bpt6k57325582/f63.imagehttp://gallica.bnf.fr/?lang=ESopen access512.554.3reducibilityvariety of complex nilpotent Lie algebrasperturbationfiliform Lie algebrairreducible componentsÁlgebra1201 Álgebra