Letters in Mathematical Physics

, Volume 8, Issue 6, pp 467–476 | Cite as

The Poincare-Dulac theorem for nonlinear representations of nilpotent lie algebras

  • Didier Arnal
  • Mabrouk Ben Ammar
  • Georges Pinczon


The aim of this Letter is to show that the Poincare-Dulac theorem for holomorphic finite-dimensional representation, is valid for any nilpotent Lie algebrag. We reduce the classification problem of representations with a semisimple linear part satisfying the Poincaré condition to an algebraic problem. We develop a complete computation in a particular case.


Statistical Physic Group Theory Classification Problem Linear Part Nonlinear Representation 
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Copyright information

© D. Reidel Publishing Company 1984

Authors and Affiliations

  • Didier Arnal
    • 1
  • Mabrouk Ben Ammar
    • 2
  • Georges Pinczon
    • 2
  1. 1.UER Sciences MathématiquesUniversité de Nancy IVandoeuvres Les Nancy CedexFrance
  2. 2.Physique MathématiqueUniversité de DijonDijon CedexFrance

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