Frame Stabilizers for framed vertex operator algebras associated to lattices having 4-frames

TL;DR

This paper investigates the structure and stabilizers of Virasoro frames in lattice vertex operator algebras, utilizing linear codes over  and , with applications to notable VOAs like E8 and moonshine.

Contribution

It introduces methods to compute frame stabilizers for lattice VOAs using  and  codes, advancing understanding of their symmetries and automorphisms.

Findings

Determined frame stabilizers for several Virasoro frames of V_{E_8}

Computed frame stabilizers for frames in the moonshine VOA

Established connections between code structures and VOA symmetries

Abstract

In this paper, we study certain Virasoro frames for lattice vertex operator algebras and their $\Z_2$-orbifolds using linear codes over $\Z_4$. We also compute the corresponding frame stabilizer from the view point of binary codes and $\Z_4$-codes. As an application, we determine the frame stabilizers of several Virasoro frames of the vertex operator algebra $V_{E_8}$ and the moonshine vertex operator algebra $V^\natural$.