Sur la classification des algèbres de Lie nilpotentes de dimension 7

Abstract

The authors give an approach to the classification of 7-dimensional nilpotent algebras. They illustrate the use of the invariant of nilpotent Lie algebras, called characteristic sequence, and defined by the maximum of the ordered sequences of the similitude exponents of the nilpotent operators ad X with X in the complementary of the first derived algebra. The classification described in this paper is given by considering a fixed characteristic sequence. To illustrate this approach, one gives the classification of 7-dimensional complex nilpotent Lie algebras corresponding to the following sequences: (6,1) (filiforme case) and (5,1,1). Other cases and the complete proofs are given in a preprint edited by I.R.M.A Strasbourg (France).