Quasi-translations and counterexamples to the Homogeneous Dependence Problem
Quasi-translations and counterexamples to the Homogeneous Dependence Problem
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DOI：
10.1090/s0002-9939-06-08335-3
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发表时间：
2006-05
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影响因子：
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通讯作者：
M. Bondt
中科院分区：
文献类型：
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作者：
M. Bondt
本文给出了5维及以上齐次幂零雅可比的线性依赖问题的反例。这个问题已经被几位作者表述为与雅可比猜想有关的猜想/问题。在10维及以上，给出了立方反例。在构造这些反例时，作者利用了所谓的拟平移，这是一种特殊类型的可逆多项式映射。拟平移也可以看作是局部幂零导子的一种特殊类型。
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.