Nonmeromorphic operator product expansion and C_2-cofiniteness for a family of W-algebras

Abstract

We prove the existence and associativity of the nonmeromorphic operator product expansion for an infinite family of vertex operator algebras, the triplet W-algebras, using results from P(z)-tensor product theory. While doing this, we also show that all these vertex operator algebras are C_2-cofinite.

21 pages, to appear in J. Phys. A: Math. Gen.; the exposition is improved and one reference is added

References in corpus (2)

• A theory of tensor products for vertex operator algebra satsifying C_2-cofiniteness
• A Z_2-orbifold model of the symplectic fermionic vertex operator superalgebra

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• The N=1 triplet vertex operator superalgebras
• Lusztig limit of quantum sl(2) at root of unity and fusion of (1,p) Virasoro logarithmic minimal models
• On Verlinde-Like Formulas in c_{p,1} Logarithmic Conformal Field Theories
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• Ribbon tensor structure on the full representation categories of the singlet vertex algebras
• A Z_2-orbifold model of the symplectic fermionic vertex operator superalgebra
• Toward logarithmic extensions of ^sl(2)_k conformal field models
• Quantum SL(2) and logarithmic vertex operator algebras at (p,1)-central charge
• Critical dense polymers with Robin boundary conditions, half-integer Kac labels and ${\mathbb{Z}}_4$ fermions
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• Towards the Construction of Local Logarithmic Conformal Field Theories
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• Hopf algebras and finite tensor categories in conformal field theory
• Characters of coinvariants in (1,p) logarithmic models
• Cofiniteness conditions, projective covers and the logarithmic tensor product theory
• Indecomposable Representations in Z_n Symmetric b,c Ghost Systems via Deformations of the Virasoro Field