An analogue of Longo's canonical endomorphism for bimodule theory and its application to asymptotic inclusions

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Abstract

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.

Original languageEnglish
Pages (from-to)249-265
Number of pages17
JournalInternational Journal of Mathematics
Volume8
Issue number2
DOIs
Publication statusPublished - Jan 1 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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