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

Shestakov, Ivan; Umirbaev, Ualbai

doi:10.1090/S0894-0347-03-00440-5

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.

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