An algebraic characterization of the affine three space

TL;DR

This paper provides algebraic characterizations of affine 2-space and 3-space over algebraically closed fields of characteristic zero by employing a variant of the Makar-Limanov invariant.

Contribution

It introduces a new algebraic approach using a variant of the Makar-Limanov invariant to characterize affine spaces of dimensions two and three.

Findings

Algebraic characterization of affine 2-space

Algebraic characterization of affine 3-space

Use of a variant of the Makar-Limanov invariant

Abstract

In this paper we give algebraic characterizations of the affine $2$-space and the affine $3$-space over an algebraically closed field of characteristic zero, using a variant of the Makar-Limanov invariant.