## Quasi-translations and counterexamples to the Homogeneous Dependence Problem

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**134**(2006), 2849-2856 Request permission

## 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.## References

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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
- 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
- © Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**134**(2006), 2849-2856 - MSC (2000): Primary 14R15, 14R20, 14R99
- DOI: https://doi.org/10.1090/S0002-9939-06-08335-3
- MathSciNet review: 2231607