Author

Chao Ma

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Preprint Oct 2026

The Derived Algebra of Nonlinear Polynomial Divergence-Free Vector Fields

We study the Lie algebra $L_{\ge2}$ of divergence-free polynomial vector fields on $k^n$, $n\ge3$, with coefficients of degree at least two, graded by coefficient degree. Over every field its derived algebra in degree $d\ge3$ is the space of exact fields, those whose contraction with the volume form is an exact form, a...

Chao Ma · 2 citations

Preprint Sep 2026

Extremal Derived Length in the Unipotent Radicals of Cartan-Type Automorphism Groups

Over perfect fields of characteristic $p\ge5$, the unipotent radicals of the height-one special, Witt-Jacobson, and Hamiltonian automorphism groups in at least three, two, and four variables, respectively, attain the largest derived length allowed by their nilpotency classes. More strongly, every term of each derived s...

Chao Ma · 1 citation