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 $H = (u(x,y), u_2(x,y,x_3), \ldots, u_{n-1}(x,y,x_n), h(x,y))$ 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.

中文翻译：

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任何维度上的一类新的幂零雅可比矩阵

具有某种结构的幂零 Jacobian 的分类因其与 Jacobian 猜想的关系而成为研究的对象。在本文中，我们将维度 $n$ 的多项式映射分类为 $H = (u(x,y), u_2(x,y,x_3), \ldots, u_{n-1}(x,y, x_n), h(x,y))$ 与 $JH$ 幂零。另外我们证明了$X+H$映射是可逆的，这表明对于这种映射，雅可比猜想得到了验证。