# Q-systems and extensions of completely unitary vertex operator algebras

## TL;DR

This paper explores the relationship between extensions of completely unitary vertex operator algebras (VOAs) and Q-systems, demonstrating that unitary extensions preserve complete unitarity.

## Contribution

It establishes a connection between VOA extensions and Q-systems and proves that unitary extensions of completely unitary VOAs are themselves completely unitary.

## Key findings

- Extensions of completely unitary VOAs correspond to (commutative) Q-systems.
- Any unitary extension of a completely unitary VOA remains completely unitary.
- The work provides a structural understanding of VOA extensions in the context of operator algebras.

## Abstract

We relate extensions of completely unitary VOAs and (commutative) Q-systems. As an application, we show that any unitary extension of a completely unitary VOA is completely unitary.