On isomorphism problems for vertex operator algebras associated with even lattices

TL;DR

This paper classifies isomorphism classes of lattice vertex operator algebras and their fixed subalgebras, providing comprehensive results for even lattices and related code-based structures.

Contribution

It offers a complete determination of isomorphism classes for lattice VOAs and their fixed subalgebras, extending to lattices linked with binary codes.

Findings

Complete classification of lattice VOA isomorphism classes

Identification of fixed subalgebras under lattice automorphisms

Results applicable to lattices from binary codes

Abstract

In this article, we completely determine the isomorphism classes of lattice vertex operator algebras and the vertex operator subalgebras fixed by a lift of the -1-isometry of the lattice. We also provide similar results for certain even lattices associated with doubly-even binary codes.