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The Poincaré-Dulac theorem for nonlinear representations of nilpotent Lie algebras. (English) Zbl 0559.17006

The authors prove (”nonlinear Poincaré-Dulac theorem”): A nonlinear, holomorphic representation of a complex nilpotent Lie algebra which satisfies the Poincaré condition (0 does not belong to the convex hull of the weights of its linear part) is holomorphically equivalent to a polynomial representation. Several consequences and applications are given.
Reviewer: W.Rossmann

MSC:

17B30 Solvable, nilpotent (super)algebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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