Le rang du systeme linéaire des racines d'une algèbre de Lie rigide résoluble complexe

Abstract

One knows that a solvable rigid Lie algebra is algebraic and can be written as a semidirect product of the form g=T⊕n if n is the maximal nilpotent ideal and T a torus on n . The main result of the paper is equivalent to the following: If g is rigid then T is a maximal torus on n . The authors then study algebras of this form where n is a filiform nilpotent algebra. A classification of this law is given in the case in which the weights of T are kα , with 1≤k≤n=dimn .