Braided Tensor Categories and Extensions of Vertex Operator Algebras |
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Authors: | Yi-Zhi Huang,Alexander Kirillov Suffix" >Jr.,James Lepowsky |
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Affiliation: | 1.Department of Mathematics,Rutgers University,Piscataway,USA;2.Department of Mathematics,State University of New York at Stony Brook,Stony Brook,USA |
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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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