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Logarithmic tensor category theory, II: Logarithmic formal calculus and properties of logarithmic intertwining operators

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arxiv 1012.4196 v2 pith:WBXIIY4Z submitted 2010-12-19 math.QA hep-thmath.RT

Yi-Zhi Huang , James Lepowsky , Lin Zhang This is my paper · ORCID
classification math.QAhep-thmath.RT
keywords logarithmiccalculuscategorydevelopformalintertwiningoperatorspart
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This is the second 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 II), we develop logarithmic formal calculus and study logarithmic intertwining operators.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Cocompletions for non-abelian vertex tensor categories

    math.QA 2026-06 unverdicted novelty 7.0 of 10

    Braided monoidal structures on C1-cofinite V-modules extend uniquely and naturally to their filtered colimit completions within generalized V-modules.

  2. Cofiniteness for Twisted Fusion Products in Vertex Operator Algebra Theory

    math.QA 2025-11 conditional novelty 7.0 of 10

    Fusion of two C1-cofinite twisted modules of a vertex operator algebra preserves C1-cofiniteness and produces a generalized twisted module satisfying the universal fusion property.

  3. Finiteness and Construction of Internal Hom for Vertex Operator Algebras

    math.QA 2026-06 unverdicted novelty 6.0 of 10

    Constructs the internal Hom object in the tensor category of restricted V-modules and proves finiteness properties and fusion rule finiteness under C1-cofiniteness.

  4. How are pseudo-$q$-traces related to (co)ends?

    math.QA 2025-08 conditional novelty 6.0 of 10

    The pseudo-q-trace construction is shown to be the same, through the sewing-factorization theorem, as the categorical end over the module category, proving conjectures of Gainutdinov-Runkel and Arike-Nagatomo.

  5. A basis theorem for Genus-One Conformal Blocks and modular invariance of intertwining operators

    math.QA 2025-08 unverdicted novelty 6.0 of 10

    Trace functions of intertwining operators form a global frame of genus-one conformal blocks, yielding a uniform proof of modular invariance for rational vertex operator algebras.

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