Classification of Ising vectors in the vertex operator algebra $V_L^+$

TL;DR

This paper classifies all Ising vectors in the vertex operator algebra $V_L^+$ derived from even lattices without roots, providing a comprehensive understanding of their structure.

Contribution

It offers the first complete classification of Ising vectors in $V_L^+$ for lattices without roots, advancing the understanding of VOA structures.

Findings

All Ising vectors in $V_L^+$ are classified.

The classification applies to lattices without roots.

Results contribute to the theory of vertex operator algebras.

Abstract

Let $L$ be an even lattice without roots. In this article, we classify all Ising vectors in the vertex operator algebra $V_L^+$ associated with $L$.