Logarithmic tensor category theory, V: Convergence condition for intertwining maps and the corresponding compatibility condition

Abstract

This is the fifth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part V), we study products and iterates of intertwining maps and of logarithmic intertwining operators and we begin the development of our analytic approach.

Part V of a series of 8 papers generalizing the results in and collectively replacing arXiv:0710:2687, with new titles. 49 pages. Trivial changes, including a piece of notation. Minor changes

References in corpus (6)

• Logarithmic tensor category theory, II: Logarithmic formal calculus and properties of logarithmic intertwining operators
• Logarithmic tensor category theory, VI: Expansion condition, associativity of logarithmic intertwining operators, and the associativity isomorphisms
• Logarithmic tensor category theory, VIII: Braided tensor category structure on categories of generalized modules for a conformal vertex algebra
• Logarithmic tensor category theory, VII: Convergence and extension properties and applications to expansion for intertwining maps
• Logarithmic tensor category theory, III: Intertwining maps and tensor product bifunctors
• Logarithmic tensor category theory, IV: Constructions of tensor product bifunctors and the compatibility conditions

Cited by in corpus (37)

• Logarithmic Conformal Field Theory: a Lattice Approach
• Schur-Weyl Duality for Heisenberg Cosets
• Lattice fusion rules and logarithmic operator product expansions
• Simple current extensions beyond semi-simplicity
• Logarithmic tensor category theory, II: Logarithmic formal calculus and properties of logarithmic intertwining operators
• Logarithmic tensor category theory, VI: Expansion condition, associativity of logarithmic intertwining operators, and the associativity isomorphisms
• Logarithmic conformal field theory, log-modular tensor categories and modular forms
• Logarithmic tensor category theory, VIII: Braided tensor category structure on categories of generalized modules for a conformal vertex algebra
• Logarithmic tensor category theory, VII: Convergence and extension properties and applications to expansion for intertwining maps
• Logarithmic tensor category theory, III: Intertwining maps and tensor product bifunctors
• Logarithmic tensor category theory, IV: Constructions of tensor product bifunctors and the compatibility conditions
• On the tensor structure of modules for compact orbifold vertex operator algebras
• The Nichols algebra of screenings
• Cosets, characters and fusion for admissible-level $\mathfrak{osp}(1|2)$ minimal models
• Kazhdan-Lusztig equivalence and fusion of Kac modules in Virasoro logarithmic models
• Twisted modules and $G$-equivariantization in logarithmic conformal field theory
• Bosonic ghostbusting -- The bosonic ghost vertex algebra admits a logarithmic module category with rigid fusion
• Modularity of logarithmic parafermion vertex algebras
• Logarithmic ^sl(2) CFT models from Nichols algebras. 1
• Free field realization of the twisted Heisenberg-Virasoro algebra at level zero and its applications
• On the applicability of logarithmic tensor category theory
• Logarithmic Intertwining Operators and Genus-One Correlation Functions
• Correspondences of categories for subregular W-algebras and principal W-superalgebras
• On semisimplicity of module categories for finite non-zero index vertex operator subalgebras
• Structure of Virasoro tensor categories at central charge $13-6p-6p^{-1}$ for integers $p>1$
• Tensor products of strongly graded vertex algebras and their modules
• Fusion in the entwined category of Yetter--Drinfeld modules of a rank-1 Nichols algebra
• C_2-cofinite W-algebras and their logarithmic representations
• A general mirror equivalence theorem for coset vertex operator algebras
• Representation theory of $L_k\left(\mathfrak{osp}(1|2)\right)$ from vertex tensor categories and Jacobi forms
• Tensor Categories arising from the Virasoro Algebra
• On rationality for $C_2$-cofinite vertex operator algebras
• Differential equations and logarithmic intertwining operators for strongly graded vertex algebras
• Duality structures for module categories of vertex operator algebras and the Feigin Fuchs boson
• The quantum group dual of the first-row subcategory for the generic Virasoro VOA
• False Theta Functions and the Verlinde formula
• Intertwining operators among twisted modules associated to not-necessarily-commuting automorphisms