ON THE RANGE OF THE INDEX OF SUBFACTORS

Autor(en): REHREN, KH
Stichwörter: ALGEBRAS; BRAID GROUP STATISTICS; Mathematics; QUANTUM-FIELDS
Erscheinungsdatum: 1995
Herausgeber: ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS
Journal: JOURNAL OF FUNCTIONAL ANALYSIS
Volumen: 134
Ausgabe: 1
Startseite: 183
Seitenende: 193
Zusammenfassung: 
A simple numerical argument is given that the minimal (Jones) index of a subfactor Nsubset of>M is strongly restricted if for L subset of N with the same index, the subfactor L subset of M contains a sector with index from the Jones series 4 cos(2) pi/m. E.g., N subset of M might be the Jones extension of, or isomorphic with, L subset of N. As a corollary extending results of Longo, the range of the index of braided endomorphisms is completely computed up to the value Ind=6. An algebraic version of the argument is outlined and is expected to generalize to braided endomorphisms the square of which contains a sector with index from the Hecke or Birman-Wenzl-Murakami series. This would allow to push the determination of the range of the index beyond 6. (C) 1995 Academic Press, Inc.
ISSN: 00221236
DOI: 10.1006/jfan.1995.1141

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