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 $k \ge 2$. Our argument is 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.
Funding Statement
The first author was partially supported by JSPS KAKENHI grant No.17H01086 and No.17K18724. The third author was partially supported by JSPS KAKENHI grant No.19K03409.
Citation
Tomoyuki ARAKAWA. Hiromichi YAMADA. Hiroshi YAMAUCHI. "$\mathbb{Z}_k$-code vertex operator algebras." J. Math. Soc. Japan 73 (1) 185 - 209, January, 2021. https://doi.org/10.2969/jmsj/83278327
Information