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.

arXiv comment21 pages, to appear in J. Phys. A: Math. Gen.; the exposition is improved and one reference is added

References in corpus (9)

• Modular invariance of trace functions in orbifold theory
• Bits and Pieces in Logarithmic Conformal Field Theory
• A Rational Logarithmic Conformal Field Theory
• An algebraic approach to logarithmic conformal field theory
• On Modular Invariant Partition Functions of Conformal Field Theories with Logarithmic Operators
• On Reducible but Indecomposable Representations of the Virasoro Algebra
• Rationality, quasirationality and finite W-algebras
• 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

Cited by in corpus (48)

• Logarithmic extensions of minimal models: characters and modular transformations
• Logarithmic Conformal Field Theory: Beyond an Introduction
• Virasoro representations and fusion for general augmented minimal models
• The tensor structure on the representation category of the ${\mathcal{W}}_p$ triplet algebra
• Logarithmic torus amplitudes
• The Triplet Vertex Operator Algebra W(p) and the Restricted Quantum Group at Root of Unity
• From boundary to bulk in logarithmic CFT
• Simple current extensions beyond semi-simplicity
• Logarithmic tensor product theory for generalized modules for a conformal vertex algebra, Part I
• Fusion rules and boundary conditions in the c=0 triplet model
• Logarithmic conformal field theory, log-modular tensor categories and modular forms
• The logarithmic triplet theory with boundary
• The N=1 triplet vertex operator superalgebras
• Generalized twisted modules associated to general automorphisms of a vertex operator algebra
• Lusztig limit of quantum sl(2) at root of unity and fusion of (1,p) Virasoro logarithmic minimal models
• A quasi-Hopf algebra for the triplet vertex operator algebra
• Symplectic fermions and a quasi-Hopf algebra structure on ${\bar{U}}_{i}sl(2)$
• On Verlinde-Like Formulas in c_{p,1} Logarithmic Conformal Field Theories
• Tensor categories and the mathematics of rational and logarithmic conformal field theory
• The Nichols algebra of screenings
• Fusion Rules of the ${\mathcal{W}}_{p,q}$ Triplet Models
• On the triplet vertex algebra W(p)
• On ribbon categories for singlet vertex algebras
• Modularity of logarithmic parafermion vertex algebras
• Logarithmic ^sl(2) CFT models from Nichols algebras. 1
• Fermionic Expressions for the Characters of c(p,1) Logarithmic Conformal Field Theories
• Ribbon tensor structure on the full representation categories of the singlet vertex algebras
• Logarithmic conformal field theories of type $B_n,\ell =4$ and symplectic fermions
• 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
• Structure of Virasoro tensor categories at central charge $13-6p-6p^{-1}$ for integers $p>1$
• Critical dense polymers with Robin boundary conditions, half-integer Kac labels and ${\mathbb{Z}}_4$ fermions
• Notes on Generalised Nullvectors in logarithmic CFT
• Zhu's algebras, $C_2$-algebras and abelian radicals
• What the characters of irreducible subrepresentations of Jordan cells can tell us about LCFT
• Towards the Construction of Local Logarithmic Conformal Field Theories
• Graph fusion algebras of WLM(p,p')
• C_2-cofinite W-algebras and their logarithmic representations
• W-extended Kac representations and integrable boundary conditions in the logarithmic minimal models WLM(1,p)
• Lattice construction of logarithmic modules for certain vertex algebras
• Hopf algebras and finite tensor categories in conformal field theory
• A Heisenberg double addition to the logarithmic Kazhdan--Lusztig duality
• Characters of coinvariants in (1,p) logarithmic models
• Cofiniteness conditions, projective covers and the logarithmic tensor product theory
• False Theta Functions and the Verlinde formula
• Quantum-sl(2) action on a divided-power quantum plane at even roots of unity
• Indecomposable Representations in Z_n Symmetric b,c Ghost Systems via Deformations of the Virasoro Field