{"product_id":"9781470467241-tensor-categories-for-vertex-operat","title":"Tensor Categories for Vertex Operator Superalgebra Extensions","description":"\u003cmeta content=\"text\/html; charset=utf-8\" http-equiv=\"Content-Type\"\u003e\u003cp\u003e\u003cspan\u003eOur main result is that the Huang-Kirillov-Lepowsky isomorphism of categories between local (super)algebra modules and extended vertex operator (super)algebra modules is also an isomorphism of braided monoidal (super)categories. We show that induction from a suitable subcategory of \u003ci\u003eV\u003c\/i\u003e-modules to \u003ci\u003eA\u003c\/i\u003e-modules is a vertex tensor functor.\u003cbr\u003eLet V be a vertex operator algebra with a category C of (generalized) modules that has vertex tensor category structure, and thus braided tensor category structure, and let A be a vertex operator (super)algebra extension of V . We employ tensor categories to study untwisted (also called local) A-modules in C, using results of Huang-Kirillov-Lepowsky that show that A is a (super)algebra object in C and that generalized A-modules in C correspond exactly to local modules for the corresponding (super)algebra object. Both categories, of local modules for a C-algebra and (under suitable conditions) of generalized A-modules, have natural braided monoidal category structure, given in the first case by Pareigis and Kirillov-Ostrik and in the second case by Huang-Lepowsky-Zhang.\u003cbr\u003e\u003cbr\u003eOur main result is that the Huang-Kirillov-Lepowsky isomorphism of categories between local (super)algebra modules and extended vertex operator (super)algebra modules is also an isomorphism of braided monoidal (super)categories. Using this result, we show that induction from a suitable subcategory of V -modules to Amodules is a vertex tensor functor. Two applications are given: First, we derive Verlinde formulae for regular vertex operator superalgebras and regular 1 2Z-graded vertex operator algebras by realizing them as (super)algebra objects in the vertex tensor categories of their even and Z-graded components, respectively.\u003cbr\u003e\u003cbr\u003e\u003c\/span\u003e\u003c\/p\u003e","brand":"Rarewaves","offers":[{"title":"Default Title","offer_id":54845444456822,"sku":"9781470467241","price":68.38,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0092\/7504\/8033\/files\/orig_36016634_46f676e2-85ac-4cea-a5bc-1e5227eb1af1.jpg?v=1757557712","url":"https:\/\/www.rarewaves.com\/products\/9781470467241-tensor-categories-for-vertex-operat","provider":"Rarewaves.com","version":"1.0","type":"link"}