Translator Disclaimer
January, 2021 $\mathbb{Z}_k$-code vertex operator algebras
Tomoyuki ARAKAWA, Hiromichi YAMADA, Hiroshi YAMAUCHI
J. Math. Soc. Japan 73(1): 185-209 (January, 2021). DOI: 10.2969/jmsj/83278327

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

Download 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

Received: 8 September 2019; Published: January, 2021
First available in Project Euclid: 10 October 2020

Digital Object Identifier: 10.2969/jmsj/83278327

Subjects:
Primary: 17B69
Secondary: 17B67

Rights: Copyright © 2021 Mathematical Society of Japan

JOURNAL ARTICLE
25 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.73 • No. 1 • January, 2021
Back to Top