Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arnold, V., Chapitres supplémentaires de la théorie des équations différentielles ordinaires, Editions Mir, Moscow, 1978.
Ben Ammar, M., ‘Nonlinear Representations of Connected Nilpotent Real Lie Groups, Lett. Math. Phys. 8, 119 (1984).
Bourbaki, N., Eléments de Mathématiques, Fasc. XXVI, Groupes et Algèbres de Lie, Chap. I. Hermann, Paris, 1971.
Brjuno, A., ‘Forme analytique des équations différentielles’, Trandy MMO 25, 119–262 (1971).
Chen, K.T., ‘Equivalence and Decomposition of Vector Fields about an Elementary Critical Point’, Amer. J. Math. 85, 693 (1963).
Flato, M., Pinczon, G., and Simon, J., ‘Nonlinear Representations of Lie Groups’, Ann. Sci. Ec. Norm. Sup. Paris, 4e serie, 10, 405 (1977).
Guillemin, V. and Sternberg, S., ‘Remarks on a Paper of Hermann’, Trans. Amer. Math. Soc. 130, 110 (1968).
Pinczon, G., ‘Nonlinear Multipliers and Applications’, to be published in Pacific J. Math.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Arnal, D., Ben Ammar, M. & Pinczon, G. The Poincare-Dulac theorem for nonlinear representations of nilpotent lie algebras. Lett Math Phys 8, 467–476 (1984). https://doi.org/10.1007/BF00400976
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00400976