
Journal of Lie Theory 29 (2019), No. 2, 391412 Copyright Heldermann Verlag 2019 There are No Rigid Filiform Lie Algebras of Low Dimension Paulo Tirao CIEMFaMAF, Universidad Nacional, Córdoba, Argentina ptirao@famaf.unc.edu.ar Sonia Vera CIEMFaMAF, Universidad Nacional, Córdoba, Argentina svera@famaf.unc.edu.ar We prove that there are no rigid complex filiform Lie algebras in the variety of (filiform) Lie algebras of dimension less than or equal to 11. More precisely we show that in any Euclidean neighborhood of a filiform Lie bracket (of low dimension), there is a nonisomorphic filiform Lie bracket. This follows by constructing nontrivial linear deformations in a Zariski open dense set of the variety of filiform Lie algebras of dimension 9, 10 and 11 (in lower dimensions this is well known.) Keywords: Filiform Lie algebras, deformations, Vergne's conjecture. MSC: 17B30, 17B99 [ Fulltextpdf (143 KB)] for subscribers only. 