# Rational vertex operator algebras are finitely generated

@article{Dong2008RationalVO,
title={Rational vertex operator algebras are finitely generated},
author={Chongying Dong and Wei Zhang},
journal={arXiv: Quantum Algebra},
year={2008}
}
• Published 13 June 2008
• Mathematics
• arXiv: Quantum Algebra
8 Citations

### SOME FINITE PROPERTIES FOR VERTEX OPERATOR SUPERALGEBRAS

• Mathematics
• 2011
Vertex operator superalgebras are studied and various results on rational Vertex operator superalgebras are obtained. In particular, the vertex operator super subalgebras generated by the weight 1/2

### Lattice Subalgebras of Strongly Regular Vertex Operator Algebras

We prove a sharpened version of a conjecture of Dong–Mason about lattice subalgebras of a strongly regular vertex operator algebra V, and give some applications. These include the existence of a

### Parafermion vertex operator algebras

• Mathematics
• 2011
This paper reviews some recent results on the parafermion vertex operator algebra associated to the integrable highest weight module L(k, 0) of positive integer level k for any affine Kac-Moody Lie

### The varieties of Heisenberg vertex operator algebras

• Mathematics
• 2015
For a vertex operator algebra V with conformal vector ω, we consider a class of vertex operator subalgebras and their conformal vectors. They are called semi-conformal vertex operator subalgebras and

### Vertex operator algebras and weak Jacobi forms

• Mathematics
• 2011
Let $V$ be a strongly regular vertex operator algebra. For a state $h \in V_1$ satisfying appropriate integrality conditions, we prove that the space spanned by the trace functions

### Moduli spaces of conformal structures on Heisenberg vertex algebras

• Mathematics
• 2018
This paper is a continuation to understand Heisenberg vertex algebras in terms of moduli spaces of their conformal structures. We study the moduli space of the conformal structures on a Heisenberg

## References

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Abstract We give a natural extension of the notion of the contragredient module for a vertex operator algebra. By using this extension we prove that for regular vertex operator algebras, Zhu's C 2

### Rational vertex operator algebras and the effective central charge

• Mathematics
• 2002
We establish that the Lie algebra of weight 1 states in a (strongly) rational vertex operator algebra is reductive, and that its Lie rank 1 is bounded above by the effective central charge c~. We

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• Mathematics
• 2001
We investigate the general structure of the automorphism group and the Lie algebra of derivations of a finitely generated vertex operator algebra. The automorphism group is isomorphic to an algebraic

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• Mathematics
• 1998
This paper gives an analogue of Ag(V) theory for a vertex operator superalgebra V and an automorphism g of finite order. The relation between the g-twisted V-modules and Ag(V)-modules is established.

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We construct an irrational C_2-cofinite vertex operator algebra associatted to a finite dimensional vector space with a nondegenerate skew-symmetric bilinear form. We also classify its equivalence

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• Mathematics
• 1998
Abstract Minimal generating subspaces of “weak PBW type” for vertex operator algebras are studied and a procedure is developed for finding such subspaces. As applications, some results on generalized

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• Mathematics
• 2002
We provide a rigorous mathematical foundation to the study of strongly rational, holomorphic vertex operator algebras V of central charge c = 8, 16 and 24 initiated by Schellekens. If c = 8 or 16 we

### Integrability of C_2-cofinite vertex operator algebras

• Mathematics
• 2006
The following integrability theorem for vertex operator algebras V satisfying some finiteness conditions(C_2-cofinite and CFT-type) is proved: the vertex operator subalgebra generated by a simple Lie

### Integrability of C2-cofinite vertex operator algebras

• Mathematics
• 2006
The following integrability theorem for vertex operator algebras V satisfying some finiteness conditions (C2-cofinite and CFT-type) is proved: the vertex operator subalgebra generated by a simple Lie

### Regularity of Rational Vertex Operator Algebras

• Mathematics
• 1995
Rational vertex operator algebras, which play a fundamental role in rational conformal field theory (see [BPZ] and [MS]), single out an important class of vertex operator algebras. Most vertex