Representations of vertex operator algebras and braided finite tensor categories

Details Representations of vertex operator algebras and braided finite tensor categories Representations of vertex operator algebras and braided finite tensor categories

2009-03-25

arxiv.org/abs/0903.4233v2

Mathematics

Quantum Algebra

24 pages. One remark and one footnote are added and some mistakes of terminology are corrected

Scientific paper

We discuss what has been achieved in the past twenty years on the construction and study of a braided finite tensor category structure on a suitable module category for a suitable vertex operator algebra. We identify the main difficult parts in the construction, discuss the methods developed to overcome these difficulties and present some further problems that still need to be solved. We also choose to discuss three among the numerous applications of the construction.

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