We give an analogous characterization of Longo's canonical endomorphism in the bimodule theory, and by using this, we construct an inclusion of factors of type II1 from a finite system of bimodules as a parallel construction to that of Longo-Rehren in a type III setting. When the original factors are approximately finite dimensional, we prove this new inclusion is isomorphic to the asymptotic inclusion in the sense of Ocneanu. This solves a conjecture of Longo-Rehren.
All Science Journal Classification (ASJC) codes
- 数学 (全般)