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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Tame and Wild Coordinates of $K[z][x,y]$


Authors: Vesselin Drensky and Jie-Tai Yu
Journal: Trans. Amer. Math. Soc. 353 (2001), 519-537
MSC (2000): Primary 13B25; Secondary 13B10, 13P10, 14E07
Published electronically: October 19, 2000
MathSciNet review: 1709773
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Abstract:

Let $K$ be a field of characteristic zero. We characterize coordinates and tame coordinates in $K[z][x,y]$, i.e. the images of $x$ respectively under all automorphisms and under the tame automorphisms of $K[z][x,y]$. We also construct a new large class of wild automorphisms of $K[z][x,y]$ which maps $x$ to a concrete family of nice looking polynomials. We show that a subclass of this class is stably tame, i.e. becomes tame when we extend its automorphisms to automorphisms of $K[z][x,y,t]$.


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Additional Information

Vesselin Drensky
Affiliation: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Block 8, 1113 Sofia, Bulgaria
Email: drensky@math.bas.bg

Jie-Tai Yu
Affiliation: Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
Email: yujt@hkusua.hku.hk

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02617-9
PII: S 0002-9947(00)02617-9
Keywords: Automorphisms of polynomial algebras, tame automorphisms, wild automorphisms, free generators of polynomial algebras
Received by editor(s): March 11, 1999
Published electronically: October 19, 2000
Additional Notes: The research of the first author was partially supported by Grant MM605/96 of the Bulgarian Foundation for Scientific Research.
The research of the second author was partially supported by RGC Grant HKU7126-98P and CRCG Grant 10201869.23067.25500.302.01
Article copyright: © Copyright 2000 American Mathematical Society