${\mathbb{Z}}_k$-code vertex operator algebras

Abstract

We introduce a simple, self-dual, rational, and $C_2$-cofinite vertex operator algebra of CFT-type associated with a ${\mathbb{Z}}_k$-code for $k\ge 2$ based on the ${\mathbb{Z}}_k$-symmetry among the simple current modules for the parafermion vertex operator algebra $K({\mathfrak{sl}}_2,k)$. We show that it is naturally realized as the commutant of a certain subalgebra in a lattice vertex operator algebra. Furthermore, we construct all the irreducible modules inside a module for the lattice vertex operator algebra.

22 pages

References in corpus (2)

• Construction and Classification of Holomorphic Vertex Operator Algebras
• Simple current extensions beyond semi-simplicity

Cited by in corpus (1)

• The classification of vertex operator algebras of OZ-type generated by Ising vectors of $\sigma$-type