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Logarithmic tensor category theory, VIII: Braided tensor category structure on categories of generalized modules for a conformal vertex algebra

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arxiv 1110.1931 v2 pith:YBVHRECB submitted 2011-10-10 math.QA hep-thmath.RT

Yi-Zhi Huang , James Lepowsky , Lin Zhang This is my paper · ORCID
classification math.QAhep-thmath.RT
keywords categorytensoralgebrabraidedcategoriespartstructuretheory
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This is the eighth 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 VIII), we construct the braided tensor category structure, using the previously developed results.

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Cited by 4 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. Reflection Equivariance and the Heisenberg Picture for Spaces of Conformal Blocks

    math.QA 2025-07 accept novelty 7.0 of 10

    Orientation reversal of surfaces corresponds algebraically to the modified trace, and reflection equivariant modular functors are exactly those whose circle category is modular and whose conformal blocks are the uniqu...

  3. 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.

  4. 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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