A Short Note on Polynomial Automorphisms

TL;DR

This paper constructs explicit polynomial automorphisms of affine n-space and identifies algebraic subgroups within the general polynomial group for certain dimensions over characteristic zero rings.

Contribution

It introduces explicit constructions of polynomial automorphisms and algebraic subgroups of GA_n(k) for specific n, advancing understanding of polynomial automorphism groups.

Findings

Explicit polynomial automorphisms constructed for certain n

Identification of algebraic subgroups within GA_n(k)

Applicable over arbitrary characteristic zero rings

Abstract

In this paper, we construct explicitely polynomial automorphisms of affine n-space for certain n. More precisely, we construct algebraic subgroups of the general polynomial group GA_n(k) where k is an arbitrary base ring of characteristic zero.