RT Journal Article T1 On the varieties of nilpotent Lie algebras of dimension 7 and 8 A1 Goze, Michel A1 Ancochea Bermúdez, José María AB Let Nn be the variety of n-dimensional complex nilpotent Lie algebras. We know that this algebraic variety is reducible for n≥11 and irreducible for n≤6. In this work we prove that N7 is composed of two algebraic components and that N8 is also reducible PB Elsevier Science SN 0022-4049 YR 1992 FD 1992-02-28 LK https://hdl.handle.net/20.500.14352/58430 UL https://hdl.handle.net/20.500.14352/58430 LA eng NO J.M. Ancochea Bermudez and M. Goze. Sur la classification des algèbres de Lie nilpotentes de dimension 7, C.R. Acad. Sci. Paris 302 (1086) 611-613.J.M. Ancochea Bermudez and M. Gaze, Classification des algèbres de Lie filiformes de dimension 8, Arch. Math. SO (IYXX) Sl I-525.J.M. Ancochea Bermudez and M. Goze, Classification des algèbres nilpotentes complexes de dimension 7. Arch. Math. 51 (1989) 175-185.J.M. Ancochea Bermudez and M. Goze. Sur la variété des lois nilpotentes de dimension 9, Rend. Sem. Fat. Sci. Univ. Cagliari 58 (l-2) (198X).R. Caries, Sur les algèbres de Lie caracteristiquement nilpotentes. Preprint. Univ. Poitiers, 1984.M. Goze. Perturbations of Lie algebras structures. NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 197 (1988).M. Goze and J.M. Ancochea Bermudez, Algebres de Lie rigides. Indag. Math. 8X (1985) 397-41.5.M. Goze and N. Makhlouf, Calcul du HZ( g, g) sur IBMPC. Preprint, Univ. Mulhouse, 1988.F. Grunewald and .I. O‘Halloran, Varieties of nilpotent Lie algebras of dimension less than six, J. Algebra 112 (1988) 315-325.G. Seeley, Degenerations of h-dimensional nilpotent Lit algebras on C. Comm. Algebra 18 (10)(1990) 3493-350s.M. Vcrgne. Sur la variete des lois nilpotentes, These, Paris, 1066.M. Vergne, Cohomologic des algèbres de Lie nilpotentes, Bull. Sot. Math. France 98 (1970)81-116. DS Docta Complutense RD 3 may 2024