RT Book, Section T1 Sobre el abierto de la variedad de las álgebras de Lie nilpotentes de dimensión 9, formado por las leyes filiformes A1 Ancochea Bermúdez, José María A1 Gómez Martín, José Ramón AB 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. PB Universidade de Evora YR 1991 FD 1991 LK https://hdl.handle.net/20.500.14352/60675 UL https://hdl.handle.net/20.500.14352/60675 DS Docta Complutense RD 21 abr 2025