On C-2-cofiniteness of parafermion vertex operator algebras

  title={On C-2-cofiniteness of parafermion vertex operator algebras},
  author={Chongying Dong and Qing Wang},
  journal={Journal of Algebra},
Singular Vectors and Zhu’s Poisson Algebra of Parafermion Vertex Operator Algebras
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
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Representations of certain vertex algebras, here called of CohFT-type, can be used to construct vector bundles of coinvariants and conformal blocks on moduli spaces of stable curves [DGT2]. We show
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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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We explain the appearance of Rogers-Ramanujan series inside the tensor product of two basic A2(2) -modules, previously discovered by the first author in [Feingold A.J., Some applications of vertex
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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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Rationality, regularity, and ₂-cofiniteness
We demonstrate that, for vertex operator algebras of CFT type, C 2 -cofiniteness and rationality is equivalent to regularity. For C 2 -cofinite vertex operator algebras, we show that irreducible weak
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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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Rationality, Quasirationality and Finite W-Algebras
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Vertex operator algebras (VOA) were introduced by Borcherds ( [B] ) as an axiomatic description of the ‘holomorphic part’ of a conformal field theory ( [BPZ] ). An account of the theory of vertex
Introduction to Lie Algebras and Representation Theory
Preface.- Basic Concepts.- Semisimple Lie Algebras.- Root Systems.- Isomorphism and Conjugacy Theorems.- Existence Theorem.- Representation Theory.- Chevalley Algebras and Groups.- References.-
Vertex Operator Algebras and the Monster