Non-linearizable Actions of Commutative Reductive Groups

TL;DR

This paper constructs examples of non-linearizable actions of commutative reductive algebraic groups on affine spaces over fields with quadratic extensions, expanding understanding of group actions in algebraic geometry.

Contribution

It generalizes previous constructions to produce non-linearizable actions over a broader class of fields with quadratic extensions.

Findings

Provides explicit examples of non-linearizable group actions.

Extends known results to fields with quadratic extensions.

Enhances understanding of algebraic group actions on affine spaces.

Abstract

We generalize a construction of Freudenburg and Moser-Jauslin in order to obtain an example of a non-linearizable action of a commutative reductive algebraic group on the affine space for every field of characteristic zero which admits a quadratic field extension.