Representations indecomposables de dimension finie des algebres de Lie

Abstract

Our problem is to determine which are the finite dimensional Lie algebras such that certain undercategories of the category of finite dimensional g-modules have only a finite number of indecomposable objects, up to isomorphism. As the study of the graph of g permits us to eliminate many Lie algebras, we construct it explicitely in the solvable case and indicate how to obtain it in the general case. For this, we give a characterization of the g-ideal, annihilator of the finite dimensional g-modules of height ≤2. Then it remains two types of Lie algebras which a supplementary study eliminates also. The result is: a Lie algebra g is solution of the problem if and only if its radical has dimension ≤1, and then g is uniserial.