Classification of subfactors in theory of operator algebras and its applications
Project/Area Number 
13640204

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Global analysis

Research Institution  The University of Tokyo 
Principal Investigator 
KAWAHIGASHI Asuyuki The University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (90214684)

Project Period (FY) 
2001 – 2003

Project Status 
Completed (Fiscal Year 2003)

Budget Amount *help 
¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 2003: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2002: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2001: ¥1,400,000 (Direct Cost: ¥1,400,000)

Keywords  Operator algebra / Quantum field theory / Subfactor / Conformal field theory / Modular invariant / Tensor cateeor / モジュラー不変 / subfactor / conformal field theory / alphainduction / Virasoro algebra / central charge / topological invariant / quantum field theory / braid / quantum double / LongoRehren 
Research Abstract 
I have obtained a classification result in operator algebraic approach to conformal field theory. A onedimensional conformal field theory in the operator algebraic formulation is called a conformal net, and I have shown, with Longo, that if the symmetry group is a diffeomorphism group, then the central charge of a conformal net is defined and if furthermore it is less than 1, then it is completely classified with an invariant labeled with pairs of ADE Dynkin diagrams. This is a complete solution to a well known problem. I fully use theory of alphainduction and modular invariants I have studied before. Next, I have studied classification theory of twodimensional conformal nets and obtained a complete classification result with Longo for the case with central charge less than 1. In the onedimensional classification, the diagrams D 2n+1 and E_7 did not appear, but now they. do appear. Strictly speaking, in the twodimensional classification results, I have assumptions that a net has parity symmetry and is maximal, and these two are equivalent to the condition of the muindex being 1, but these two conditions can be easily dropped, and we would have merely more combinatorial complecity. We use the abovementioned onedimensional classification for this, and the new point is theory of 2苗ohomology group of a tensor category. A key step is a proof of 2chomology vanishing for tensor categories related to the Virasoro algebra

Report
(4 results)
Research Products
(15 results)