Classification des algèbres de Lie nilpotentes complexes de dimension 7

Abstract

The authors give a complete list of the 7-dimensional complex nilpotent Lie algebras. This classification is obtained by using an invariant of nilpotent Lie algebras, called a characteristic sequence and defined by the maximum of the Segre symbols of the nilpotent linear maps ad x with x in the complement of the derived subalgebra. This invariant was introduced by them in an earlier paper [C. R. Acad. Sci. Paris Ser. I Math. 302 (1986), no. 17, 611–613; in which they determined the nilpotent complex Lie algebras corresponding to the characteristic sequences (6, 1) and (5, 1, 1). The paper under review contains no proofs; for details the authors refer to another article [the authors, “Classification des algebres de Lie nilpotentes de dimension 7”, Univ. Louis Pasteur, Strasbourg, 1986; per bibl.].