Noetherianity of twisted Zhu algebra and bimodules

TL;DR

This paper proves that for many vertex operator algebras and their modules, the associated Zhu algebras and bimodules are Noetherian, enabling algebraic geometric methods in their analysis.

Contribution

It establishes the Noetherian property for Zhu algebras and bimodules of a broad class of VOAs and their twisted variants, advancing their algebraic understanding.

Findings

Zhu algebras are Noetherian for a large class of VOAs

Bimodules associated with VOAs are Noetherian

Potential for algebraic geometric methods in VOA representation theory

Abstract

In this paper we show that for a large natural class of vertex operator algebras (VOAs) and their modules, the Zhu algebras and bimodules (and their $g$-twisted analogs) are Noetherian. These carry important information about the representation theory of the VOA, and its fusion rules, and the Noetherian property gives the potential for (non-commutative) algebro-geometric methods to be employed in their study.