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 | References | Similar Articles | Additional Information
Abstract: A characterization of tame automorphisms of the algebra ![$A=F[x_1,x_2,x_3]$](/jams/2004-17-01/S0894-0347-03-00440-5/gif-abstract0/img1.gif){kind=small}
of polynomials in three variables over a field 
of characteristic 
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 
are algorithmically recognizable.
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![$K[z][x,y]$](/jams/2004-17-01/S0894-0347-03-00440-5/gif-references0/img3.gif){kind=small}
, Trans. Amer. Math. Soc. 353 (2001), no. 2, 519-537. ![$k[x,y]$](/jams/2004-17-01/S0894-0347-03-00440-5/gif-references0/img4.gif){kind=small}
, Lectures in Math., Kyoto Univ., Kinokuniya, Tokyo, 1972. Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 13F20, 13P10, 14H37, 14R10, 14R15
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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
