Tensor Categories for Vertex Operator Superalgebra Extensions
著者
書誌事項
Tensor Categories for Vertex Operator Superalgebra Extensions
（Memoirs of the American Mathematical Society, no. 1472）
American Mathematical Society, c2024
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注記
"March 2024, volume 295, number 1472 (fourth of 6 numbers)"
Includes bibliographical references (p. 173-181)
内容説明・目次
内容説明
Let 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.
Our 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.
目次
Chapters
1. Introduction
2. Tensor Categories and Supercategories
3. Vertex Tensor Categories
4. Applications
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