THE LOCAL LINEARIZATION PROBLEM FOR SMOOTH SL(n)-ACTIONS
نویسنده
چکیده
This paper considers SL(n,R)-actions on Euclidean space fixing the origin. We show that all C-actions on R are linearizable. We give C∞-actions of SL(2,R) on R and of SL(3,R) on R which are not linearizable. We classify the C-actions of SL(n,R) on R. Finally, the paper concludes with a study of the linearizability of SL(n,Z)-actions. RÉSUMÉ. Dans cet article, on considère les actions de SL(n,R) sur l’espace euclidien qui fixent l’origine. On montre que les actions C sur R sont linéarisables. On donne des actions C∞ de SL(2,R) sur R et de SL(3,R) sur R qui ne sont pas linéarisables. On classifie les actions C de SL(n,R) sur R. L’article s’achève par une étude de la linéarisabilité des actions de SL(n,Z).
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