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Proceedings of the American Mathematical Society

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Quasi-translations and counterexamples to the Homogeneous Dependence Problem


Author: Michiel de Bondt
Journal: Proc. Amer. Math. Soc. 134 (2006), 2849-2856
MSC (2000): Primary 14R15, 14R20, 14R99
Published electronically: May 2, 2006
MathSciNet review: 2231607
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Abstract: In this article, the author gives counterexamples to the Linear Dependence Problem for Homogeneous Nilpotent Jacobians for dimension 5 and up. This problem has been formulated as a conjecture/problem by several authors in connection to the Jacobian conjecture. In dimension 10 and up, cubic counterexamples are given.

In the construction of these counterexamples, the author makes use of so-called quasi-translations, a special type of invertible polynomial maps. Quasi-translations can also be seen as a special type of locally nilpotent derivations.


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Additional Information

Michiel de Bondt
Affiliation: Department of Mathematics, Radboud University, Postbus 9010, 6500 GL Nijmegen, The Netherlands
Email: debondt@math.ru.nl

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08335-3
Keywords: Jacobian (conjecture), quasi-translation, linear dependence problem
Received by editor(s): October 5, 2004
Received by editor(s) in revised form: April 27, 2005
Published electronically: May 2, 2006
Additional Notes: The author was supported by the Netherlands Organization of Scientific Research (NWO)
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.