Finite-dimensional vertex algebra modules over fixed point differential subfields

TL;DR

This paper proves that all finite-dimensional modules over fixed point subfields of differential fields can be embedded into twisted modules over the larger field, advancing the understanding of module structures in vertex algebra theory.

Contribution

It establishes that every finite-dimensional vertex algebra module over the fixed point subfield can be realized within a twisted module over the original differential field.

Findings

Every finite-dimensional $K^G$-module embeds into a twisted $K$-module.

The result connects modules over fixed point subfields to twisted modules over the original field.

Provides a structural understanding of modules in the context of differential fields and automorphism groups.

Abstract

Let $K$ be a differential field over $\C$ with derivation $D$, $G$ a finite linear automorphism group over $K$ which preserves $D$, and $K^G$ the fixed point subfield of $K$ under the action of $G$. We show that every finite-dimensional vertex algebra $K^G$-module is contained in some twisted vertex algebra $K$-module.