Computations of Keller maps over fields with $\frac{1}{6}$

Abstract

We classify Keller maps $x+H$ in dimension $n$ over fields with $\frac{1}{6}$, for which $H$ is homogeneous, and (1) deg $H=3$ and rk $JH\le 2$; (2) deg $H=3$ and $n\le 4$; (3) deg $H=4$ and $n\le 3$; (4) deg $H=4=n$ and $H_1,H_2,H_3,H_4$ are linearly dependent over $K$. In our proof of these classifications, we formulate (and prove) several results which are more general than needed for these classifications. One of these results is the classification of all homogeneous polynomial maps $H$ as in (1) over fields with $\frac{1}{6}$.

21 pages + Maple 8 calculations

References in corpus (2)

• The strong nilpotency index of a matrix
• Mathieu subspaces of codimension less than n of Mat_n(K)

Cited by in corpus (1)

• The classification of some polynomial maps with nilpotent Jacobians