The extensions of $L_{sl_2}(k,0)$ and preunitary vertex operator algebra with central charges $c<1$

TL;DR

This paper classifies extensions of affine vertex operator algebras and preunitary vertex operator algebras with central charges less than one, including a complete classification of unitary cases, advancing understanding of their structure.

Contribution

It provides a comprehensive classification of extensions and unitary vertex operator algebras with central charges below one, filling gaps in the structural understanding of these algebras.

Findings

Classified extensions of $L_{sl_2}(k,0)$ for $c<1$

Classified preunitary vertex operator algebras with $c<1$

Complete classification of unitary vertex operator algebras with $c<1$

Abstract

The extensions of the affine vertex operator algebras $L_{sl_2}(k,0)$ and the preunitary vertex operator algebras with central charges $c<1$ are classified. In particular, the unitary vertex operator algebras with central charges $c<1$ are classified.