$\mathbb{Z}_{2k}$-code vertex operator algebras

TL;DR

This paper constructs and classifies a class of vertex operator algebras associated with $Z_{2k}$-codes, demonstrating their module structure and realization within lattice VOAs, advancing understanding of their algebraic properties.

Contribution

It introduces a new class of $Z_{2k}$-code vertex operator algebras, classifies their irreducible modules, and connects them to lattice VOAs, providing a comprehensive structural analysis.

Findings

Constructed $Z_{2k}$-code vertex operator algebras.

Classified all irreducible modules for these algebras.

Realized modules within lattice vertex operator algebras.

Abstract

We study a simple, self-dual, rational, and $C_2$-cofinite vertex operator algebra of CFT-type whose simple current modules are graded by $\mathbb{Z}_{2k}$. Based on those simple current modules, a vertex operator algebra associated with a $\mathbb{Z}_{2k}$-code is constructed. The classification of irreducible modules for such a vertex operator algebra is established. Furthermore, all the irreducible modules are realized in a module for a certain lattice vertex operator algebra.