Vertex operator algebras, fusion rules and modular transformations

2005/02/26 by Yi-Zhi Huang, Huang, Yi-Zhi
Mathematics · Physics and Astronomy · #17B69 #18D10 #81T40 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #hep-th #math-ph #math.AG #math.MP #math.QA #msc:17B69 #msc:18D10 #msc:81T40

paper · pdf · doi:10.48550/arxiv.math/0502558

21 pages. To appear in Proceedings of the conference "Non-commutative Geometry and Representation Theory in Mathematical Physics," July 5-10, 2004, Karlstad University, Sweden

arxiv created 2005/02/26 · openalex publication_date 2005/02/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss a recent proof by the author of a general version of the Verlinde conjecture in the framework of vertex operator algebras and the application of this result to the construction of modular tensor tensor category structure on the category of modules for a vertex operator algebra.

Citations

• Classical and quantum conformal field theory

Related

• Fusion categories for affine vertex algebras at admissible levels
• Tensor products of modules for a vertex operator algebra and vertex tensor categories
• Rigidity and modularity of vertex tensor categories
• Representation theory and tensor product theory for vertex operator algebras
• Vertex operator algebras and the Verlinde conjecture