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Proceedings of the American Mathematical Society

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Minimal polynomial of an exponential automorphism of $ \mathbb{C}^n$


Author: Jakub Zygadło
Journal: Proc. Amer. Math. Soc. 137 (2009), 1849-1853
MSC (2000): Primary 14R10; Secondary 13N15
Published electronically: January 9, 2009
MathSciNet review: 2480263
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Abstract: We show that the minimal polynomial of a polynomial exponential automorphism $ F$ of $ \mathbb{C}^n$ (i.e. $ F=\exp(D)$ where $ D$ is a locally nilpotent derivation) is of the form $ \mu_F(T)=(T-1)^d$, with $ d=\min\{m\in\mathbb{N}: D^{\circ m}(X_i)=0$ for $ i=1,\ldots,n\}$.


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Additional Information

Jakub Zygadło
Affiliation: Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
Email: jakub.zygadlo@im.uj.edu.pl

DOI: https://doi.org/10.1090/S0002-9939-09-09786-X
Keywords: Polynomial automorphism, locally nilpotent derivation, minimal polynomial
Received by editor(s): January 7, 2008
Published electronically: January 9, 2009
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.