Sobre el abierto de la variedad de las álgebras de Lie nilpotentes de dimensión 9, formado por las leyes filiformes

Abstract

In this paper we prove that in N9, the variety of complex nilpotent Lie algebras of dimension 9, there exists a unique irreducible component intersecting the open subset of all filiform Lie algebras of dimension 9. It is also proved that, unlike in dimension 8 [see J. M. Ancochea-Bermudez and M. Goze, Arch. Math. (Basel) 50 (1988), no. 6, 511–525; N9 contains no rigid filiform Lie algebras.