## Journal of the Mathematical Society of Japan

### Induced modules for orbifold vertex operator algebras

Ching Hung LAM

#### Abstract

Let $V$ be a simple vertex operator algebra and $G<$ Aut $V$ a finite abelian subgroup such that $V^{G}$ is rational. We study the representations of $V$ based on certain assumptions on $V^{G}$-modules. We prove a decomposition theorem for irreducible $V$-modules. We also define an induced module from $V^{G}$ to $V$ and show that every irreducible $V$-module is a quotient module of some induced module. In addition, we prove that $V$ is rational in this case.

#### Article information

Source
J. Math. Soc. Japan, Volume 53, Number 3 (2001), 541-557.

Dates
First available in Project Euclid: 9 June 2008

https://projecteuclid.org/euclid.jmsj/1213023722

Digital Object Identifier
doi:10.2969/jmsj/05330541

Mathematical Reviews number (MathSciNet)
MR1828968

Zentralblatt MATH identifier
1002.17015

#### Citation

Hung LAM, Ching. Induced modules for orbifold vertex operator algebras. J. Math. Soc. Japan 53 (2001), no. 3, 541--557. doi:10.2969/jmsj/05330541. https://projecteuclid.org/euclid.jmsj/1213023722