# Rational vertex operator algebras and the effective central charge

@article{Dong2002RationalVO, title={Rational vertex operator algebras and the effective central charge}, author={Chongying Dong and Geoffrey Mason}, journal={International Mathematics Research Notices}, year={2002}, volume={2004}, pages={2989-3008} }

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 show that lattice vertex operator algebras may be characterized by the equalities c~=l=c, and in particular holomorphic lattice theories may be characterized among all holomorphic vertex operator algebras by the equality l = c.

## 90 Citations

### 71 holomorphic vertex operator algebras of central charge 24

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In this article, we give a survey on the recent progress towards the classification of strongly regular holomorphic vertex operator algebras of central charge 24. In particular, we review the…

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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…

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. We describe the automorphism groups of all holomorphic vertex operator algebras of central charge 24 with non-trivial weight one Lie algebras by using their constructions as simple current…

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This article is a continuation of our work on the classification of holomorphic framed vertex operator algebras of central charge 24. We show that a holomorphic framed VOA of central charge 24 is…

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We study the properties of shifted vertex operator algebras, which are vertex algebras derived from a given theory by shifting the conformal vector. In this way, we are able to exhibit large numbers…

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In this article, we describe a construction of a holomorphic vertex operator algebras of central charge 24 whose weight one Lie algebra has type $${A_{6,7}}$$A6,7.

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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…

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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…

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