A new class of Nilpotent Jacobians in any dimension

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),u2(x,y,x3),…,un−1(x,y,xn),h(x,y)) with JH nilpotent. In addition...

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Bibliographic Details
Published in:Journal of algebra 2021-01, Vol.566, p.283-301
Main Authors: Castañeda, Álvaro, van den Essen, Arno
Format: Article
Language:English
Subjects:
Jacobian conjecture
Nilpotent Jacobian matrix
Polynomial maps
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Summary: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),u2(x,y,x3),…,un−1(x,y,xn),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.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2020.08.026