Classification of local conformal nets. Case c<1

• 成果类型: Article
• 署名作者: Kawahigashi, Y; Longo, R
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2004.160.493
• 发表日期: 2004
• 页码: 493-522
• 关键词: braid group statistics; modular invariants; alpha-induction; subfactors; ALGEBRAS; REPRESENTATIONS; virasoro; FIELDS; graphs; tensor

摘要

We completely classify diffeomorphism covariant local nets of von Neumann algebras on the circle with central charge c less than 1. The irreducible ones are in bijective correspondence with the pairs of A-D-2n-E-6,E-8 Dynkin diagrams such that the difference of their Coxeter numbers is equal to 1. We first identify the nets generated by irreducible representations of the Virasoro algebra for c < 1 with certain coset nets. Then, by using the classification of modular invariants for the minimal models by Cappelli-Itzykson-Zuber and the method of a-induction in subfactor theory, we classify all local irreducible extensions of the Virasoro nets for c < 1 and infer our main classification result. As an application, we identify in our classification list certain concrete coset nets studied in the literature.