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Braided Tensor Categories and Extensions of Vertex Operator Algebras

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Abstract

Let V be a vertex operator algebra satisfying suitable conditions such that in particular its module category has a natural vertex tensor category structure, and consequently, a natural braided tensor category structure. We prove that the notions of extension (i.e., enlargement) of V and of commutative associative algebra, with uniqueness of unit and with trivial twist, in the braided tensor category of V-modules are equivalent.

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Authors and Affiliations

  1. Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd., Piscataway, NJ, 08854-8019, USA

    Yi-Zhi Huang & James Lepowsky

  2. Department of Mathematics, State University of New York at Stony Brook, Stony Brook, NY, 11794, USA

    Alexander Kirillov Jr.

Authors
  1. Yi-Zhi Huang
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  2. Alexander Kirillov Jr.
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  3. James Lepowsky
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Correspondence to Yi-Zhi Huang.

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Communicated by Y. Kawahigashi

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Huang, YZ., Kirillov, A. & Lepowsky, J. Braided Tensor Categories and Extensions of Vertex Operator Algebras. Commun. Math. Phys. 337, 1143–1159 (2015). https://doi.org/10.1007/s00220-015-2292-1

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  • DOI: https://doi.org/10.1007/s00220-015-2292-1

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