The tame and the wild automorphisms of polynomial rings in three variables
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- by Ivan P. Shestakov and Ualbai U. Umirbaev;
- J. Amer. Math. Soc. 17 (2004), 197-227
- DOI: https://doi.org/10.1090/S0894-0347-03-00440-5
- Published electronically: October 3, 2003
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Abstract:
A characterization of tame automorphisms of the algebra $A=F[x_1,x_2,x_3]$ of polynomials in three variables over a field $F$ of characteristic $0$ is obtained. In particular, it is proved that the well-known Nagata automorphism is wild. It is also proved that the tame and the wild automorphisms of $A$ are algorithmically recognizable.References
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Bibliographic Information
- Ivan P. Shestakov
- Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, São Paulo - SP, 05311–970, Brazil; Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia
- MR Author ID: 289548
- Email: shestak@ime.usp.br
- Ualbai U. Umirbaev
- Affiliation: Department of Mathematics, Eurasian National University, Astana, 473021, Kazakhstan
- Email: umirbaev@yahoo.com
- Received by editor(s): January 8, 2003
- Published electronically: October 3, 2003
- Additional Notes: The first author was supported by CNPq.
The second author was supported by the FAPESP Proc.00/06832-8. - © Copyright 2003 American Mathematical Society
- Journal: J. Amer. Math. Soc. 17 (2004), 197-227
- MSC (2000): Primary 13F20, 13P10, 14H37; Secondary 14R10, 14R15
- DOI: https://doi.org/10.1090/S0894-0347-03-00440-5
- MathSciNet review: 2015334