# Representations of vertex operator algebras

@article{Dong2006RepresentationsOV, title={Representations of vertex operator algebras}, author={Chongying Dong and Cuipo Jiang}, journal={arXiv: Quantum Algebra}, year={2006} }

This paper is an exposition of the representation theory of vertex operator algebras in terms of associative algebras A_n(V) and their bimodules. A new result on the rationality is given. That is, a simple vertex operator algebra V is rational if and only if its Zhu algebra A(V) is a semisimple associative algebra and each irreducible admissible $V$-module is ordinary.

## 3 Citations

### Bimodules associated to vertex operator algebras

- Mathematics
- 2006

Let V be a vertex operator algebra and m, n ≥ 0. We construct an An(V)-Am(V)-bimodule An,m(V) which determines the action of V from the level m subspace to level n subspace of an admissible V-module.…

### Bimodules associated to vertex operator superalgebras

- Mathematics
- 2008

Let V be a vertex operator superalgebra and m, n ∈ 1/2 ℤ+. We construct an An(V)-Am(V)-bimodule An,m(V) which characterizes the action of V from the level m subspace to level n subspace of an…

### Fusion Rules for the Lattice Vertex Operator Algebra $V_L$

- Mathematics
- 2018

Author(s): Nguyen, Danquynh | Advisor(s): Dong, Chongying | Abstract: In this thesis, we compute the fusion rules among the irreducible modules of $V_L$ - the vertex operator algebra associated with…

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- Mathematics
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