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The tame and the wild automorphisms of polynomial rings in three variables


Authors: Ivan P. Shestakov and Ualbai U. Umirbaev
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
Published electronically: October 3, 2003
MathSciNet review: 2015334
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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.


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Additional 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
Email: shestak@ime.usp.br

Ualbai U. Umirbaev
Affiliation: Department of Mathematics, Eurasian National University, Astana, 473021, Kazakhstan
Email: umirbaev@yahoo.com

DOI: https://doi.org/10.1090/S0894-0347-03-00440-5
Keywords: Rings of polynomials, automorphisms, subalgebras
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.
Article copyright: © Copyright 2003 American Mathematical Society

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