# The structure of parafermion vertex operator algebras

@article{Dong2010TheSO,
title={The structure of parafermion vertex operator algebras},
author={Chongying Dong and Ching Hung Lam and Qing Wang and Hiromichi Yamada},
journal={Journal of Algebra},
year={2010},
volume={323},
pages={371-381}
}
• Published 15 January 2010
• Mathematics
• Journal of Algebra
The Structure of Parafermion Vertex Operator Algebras: General Case
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• 2009
The structure of the parafermion vertex operator algebra associated to an integrable highest weight module for any affine Kac-Moody algebra is studied. In particular, a set of generators for this
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• 2014
The quantum dimensions and the fusion rules for the parafermion vertex operator algebra associated to the irreducible highest weight module for the affine Kac-Moody algebra A (1) 1 of level k are
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• 2014
The irreducible modules for the parafermion vertex operator algebra associated to any finite dimensional Lie algebra and any positive integer are identified, the quantum dimensions are computed and
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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
Singular Vectors and Zhu’s Poisson Algebra of Parafermion Vertex Operator Algebras
• Mathematics
• 2013
We study Zhu’s Poisson algebra of parafermion vertex operator algebras associated with integrable highest weight modules for the affine Kac-Moody Lie algebra $$\widehat{sl}_{2}$$. Using singular

## References

SHOWING 1-10 OF 27 REFERENCES
Structure of the standard modules for the affine Lie algebra A[(1)] [1]
• Mathematics
• 1985
The Lie algebra $A_1^(1)$ The category $\cal P_k$ The generalized commutation relations Relations for standard modules Basis of $\Omega_L$ for a standard module $L$ Schur functions Proof of linear
Unitary representations of the Virasoro and super-Virasoro algebras
• Mathematics
• 1986
It is shown that a method previously given for constructing representations of the Virasoro algebra out of representations of affine Kac-Moody algebras yields the full discrete series of highest
On quantum Galois theory
• Mathematics
• 1994
The goals of the present paper are to initiate a program to systematically study and rigorously establish what a physicist might refer to as the “operator content of orbifold models.” To explain what
Vertex operator algebras associated to representations of affine and Virasoro Algebras
• Mathematics
• 1992
The first construction of the integrable highest-weight representations of affine Lie algebras or loop algebras by Kac i-K] was greatly inspired by the generalization of the Weyl denominator formula
Classification of local conformal nets
• Mathematics
• 2005
We completely classify diffeomorphism covariant local nets of von Neumann algebras on the circle with central charge c less than 1. The irreducible ones are in bijective correspondence with the pairs
Classification of local conformal nets. Case c < 1
• Mathematics
Annals of Mathematics
• 2004
We completely classify diffeomorphism covariant local nets of von Neumann algebras on the circle with central charge c less than 1. The irreducible ones are in bijective correspondence with the pairs