Minimal polynomial of an exponential automorphism of $\mathbb {C}^n$
HTML articles powered by AMS MathViewer
- by Jakub Zygadło PDF
- Proc. Amer. Math. Soc. 137 (2009), 1849-1853 Request permission
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 $d=\min \{m\in \mathbb {N}: D^{\circ m}(X_i)=0\text { for } i=1,\ldots ,n\}$.References
- Jean-Philippe Furter and Stefan Maubach, Locally finite polynomial endomorphisms, J. Pure Appl. Algebra 211 (2007), no. 2, 445–458. MR 2340462, DOI 10.1016/j.jpaa.2007.02.005
- Arno van den Essen, Polynomial automorphisms and the Jacobian conjecture, Progress in Mathematics, vol. 190, Birkhäuser Verlag, Basel, 2000. MR 1790619, DOI 10.1007/978-3-0348-8440-2
- Masayoshi Nagata, On automorphism group of $k[x,\,y]$, Kinokuniya Book Store Co., Ltd., Tokyo, 1972. Department of Mathematics, Kyoto University, Lectures in Mathematics, No. 5. MR 0337962
Additional Information
- Jakub Zygadło
- Affiliation: Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
- Email: jakub.zygadlo@im.uj.edu.pl
- Received by editor(s): January 7, 2008
- Published electronically: January 9, 2009
- Communicated by: Bernd Ulrich
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 1849-1853
- MSC (2000): Primary 14R10; Secondary 13N15
- DOI: https://doi.org/10.1090/S0002-9939-09-09786-X
- MathSciNet review: 2480263