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
Quantum dimensions and fusion rules for parafermion vertex operator algebras
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
The 3-state Potts model and Rogers-Ramanujan series
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
The irreducible modules and fusion rules for the parafermion vertex operator algebras
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
Let V be a simple vertex operator algebra containing a rank n Heisenberg vertex algebra H and let C = Com(H;V) be the coset of H in V. Assuming that the module categories of interest are vertex


The structure of parafermion vertex operator algebras
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
The Structure of Parafermion Vertex Operator Algebras: General Case
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
Some finiteness properties of regular vertex operator algebras
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
W -algebras related to parafermion algebras
Rationality, Quasirationality and Finite W-Algebras
Abstract: Some of the consequences that follow from the C2 condition of Zhu are analysed. In particular it is shown that every conformal field theory satisfying the C2 condition has only finitely
Symmetric invariant bilinear forms on vertex operator algebras
Rationality of Virasoro Vertex Operator Algebras Weiqiang Wang
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