Closed subgroups of the polynomial automorphism group containing the affine subgroup

TL;DR

This paper proves that in characteristic zero, any closed subgroup of the polynomial automorphism group that contains the affine group must also contain the entire tame subgroup, revealing a structural property of these groups.

Contribution

It establishes a significant subgroup containment result, showing that such closed subgroups necessarily include the tame automorphisms, advancing understanding of polynomial automorphism groups.

Findings

Closed subgroups containing the affine group include the tame group

Structural insight into polynomial automorphism groups in characteristic zero

Clarifies subgroup relations within automorphism groups

Abstract

We prove that, in characteristic zero, closed subgroups of the polynomial automorphisms group containing the affine group contain the whole tame group.