Sub-structure in module category of Virasoro vertex operator algebras $L(c_{p,q}, 0)$

TL;DR

This paper classifies all premodular and modular tensor subcategories within the module categories of Virasoro vertex operator algebras, providing a comprehensive understanding of their sub-structural properties.

Contribution

It explicitly determines all premodular and modular tensor subcategories in the module categories of Virasoro VOAs and their simple current extensions.

Findings

All premodular subcategories identified

All modular tensor subcategories classified

Structural insights into Virasoro VOA modules

Abstract

We determine all premodular subcategories and modular tensor subcategories in the module categories of Virasoro vertex operator algebras $L(c_{p,q},0)$ and the module categories of the simple current extensions of $L(c_{p,p+1},0)$.