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arXiv · 1406.3420

Braided tensor categories and extensions of vertex operator algebras

Yi-Zhi Huang·Alexander Kirillov Jr.·James Lepowsky
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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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Yi-Zhi Huang, Alexander Kirillov Jr., James Lepowsky. 2014-06-13. Braided tensor categories and extensions of vertex operator algebras. https://doi.org/10.1007/s00220-015-2292-1

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