On the semi-regular module and vertex operator algebras

TL;DR

This paper proves a conjecture regarding the existence of canonical filtrations for a specific family of vertex operator algebras at rational levels, advancing understanding in algebraic structures related to conformal field theory.

Contribution

It establishes the existence of canonical filtrations for a class of vertex operator algebras, confirming a previously conjectured property at rational levels.

Findings

Canonical filtrations exist for the studied vertex operator algebras.

The result confirms a key conjecture in the theory of vertex operator algebras.

Advances the structural understanding of vertex operator algebras at rational levels.

Abstract

We prove a conjecture stated in a previous paper by the author about the existence of canonical filtrations for a family of vertex operator algebras in rational levels.