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.
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Loupias, M. Representations indecomposables de dimension finie des algebres de Lie. Manuscripta Math 6, 365–379 (1972). https://doi.org/10.1007/BF01303689
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DOI: https://doi.org/10.1007/BF01303689