Abstract
Let g be anilpotent Lie algebra (of finite dimensionn over an algebraically closed field of characteristic zero) and let Der(g) be the algebra of derivations of g. Thesystem of weights of g is defined as being that of the standard representation of a “maximal torus” in Der(g) (see l.l). For a fixed integern, it is well-known that there are in general uncountably many isomorphism classes of nilpotent Lie algebra of dimensionn; but we show that there arefinitely many systems of weights, and each of them is explicitely constructed. The class of those Lie algebras having a given (arbitrary) system of weights is also studied.
The first chapter is a setting for the study of nilpotent Lie algebras, used to prove some general theorems. In the second chapter, attention is restricted to a class of nilpotent Lie algebras for which our setting is particularly well adapted.
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Ce papier est extrait de mon travail de thèse [5] effectué sous la direction du Professeur Jean de Siebenthal que je remercie vivement.
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Favre, G. Systeme de poids sur une algebre de Lie nilpotente. Manuscripta Math 9, 53–90 (1973). https://doi.org/10.1007/BF01320668
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DOI: https://doi.org/10.1007/BF01320668