A new class of Nilpotent Jacobians in any dimension

JOURNAL OF ALGEBRA

卷:566

Article

Castaneda, Alvaro¹  van den Essen, Arno² 

[1] Univ Chile, Fac Ciencias, Dept Matemat, Casilla 653, Santiago, Chile

[2] Radboud Univ Nijmegen, Dept Math, Postbus 9010, NL-6500 GL Nijmegen, Netherlands

关键词: Jacobian conjecture;    Nilpotent Jacobian matrix;    Polynomial maps;   

DOI  :  10.1016/j.jalgebra.2020.08.026

来源: Elsevier

【 摘 要 】

The classification of the nilpotent Jacobians with some structure has been an object of study because of its relationship with the Jacobian conjecture. In this paper we classify the polynomial maps in dimension n of the form H = (u(x, y), u(2) (x, y, x(3)), ..., u(n-1) (x, y, x(n)), h(x, y)) with JH nilpotent. In addition we prove that the maps X + H are invertible, which shows that for this kind of maps the Jacobian conjecture is verified. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free