A characterization of the rational vertex operator algebra $V_{\Z\alpha}^{+}$}: II

TL;DR

This paper characterizes the rational vertex operator algebra $V_L^+$ for rank one lattices using dimensions of small-weight subspaces, simplifying the classification of such algebras at central charge 1.

Contribution

It provides a new characterization of $V_L^+$ for rank one lattices based on subspace dimensions, reducing the classification problem at central charge 1.

Findings

Characterization of $V_L^+$ in terms of homogeneous subspace dimensions

Reduction of classification of rational VOAs at central charge 1

Connection to the $E$-series of VOAs

Abstract

A characterization of vertex operator algebra $V_L^+$ for any rank one positive definite even lattice $L$ is given in terms of dimensions of homogeneous subspaces of small weights. This result reduces the classification of rational vertex operator algebras of central charge 1 to the characterization of three vertex operator algebras in the $E$-series of central charge one.