Selecta Mathematica

, Volume 18, Issue 4, pp 799–802 | Cite as

Stable tameness of automorphisms of \({F\langle x,y,z\rangle}\) fixing z

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Abstract

It is proved that every z-automorphism (z-coordinates, respectively) of the free associative algebra \({F\langle x,y,z\rangle}\) over an arbitrary field F is stably tame.

Keywords

Automorphisms Coordinates Polynomial algebras Free associative algebras Stably tameness Lifting problem 

Mathematics Subject Classification

Primary 13S10 16S10 Secondary 13F20 13W20 14R10 16W20 16Z05 

Notes

Acknowledgments

Jie-Tai Yu would like to thank David Wright for sending him an early version of [6] in July 2007. The authors also thank Vesselin Drensky and Leonid Makar-Limanov for their comments and remarks.

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

References

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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Institute of Core MathematicsShanghai UniversityShanghaiChina
  2. 2.Department of MathematicsBar-Ilan UniversityRamat-GanIsrael
  3. 3.Department of MathematicsThe University of Hong KongHong Kong SARChina

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