Minimal index and braided subfactors
type: Item
instance of: scholarly article
title: Minimal index and braided subfactors
zbMATH Open document ID: 0798.46047
DOI: 10.1016/0022-1236(92)90013-9
author: Roberto Longo
published in: Journal of Functional Analysis
publication date: 1993-05-02T00:00:00Z
review text: The author derives the multiplicativity of the minimal index of subfactors and applies this result to the analysis of certain braid group representations that describe symmetries of endomorphisms of factors, with sufficiently small index, abstracting the structure that emerges from the superselection sector analysis in quantum field theory. For these endomorphisms, the possible index values has several gaps besides the Jones restriction, for example, the index does not lie in the interval \((4,3\sqrt{2})\). As consequence, subfactors arising in low- dimensional QFT cannot be arbitrary.
Mathematics Subject Classification ID: 46L37
Mathematics Subject Classification ID: 81T10
Mathematics Subject Classification ID: 46L60
zbMATH DE Number: 152023
zbMATH Keywords: multiplicativity of the minimal index of subfactors
zbMATH Keywords: braid group representations
zbMATH Keywords: symmetries of endomorphisms of factors
zbMATH Keywords: superselection sector analysis in quantum field theory
zbMATH Keywords: subfactors
zbMATH Keywords: low-dimensional QFT
reviewed by: V. Ya. Golodets
MaRDI profile type: Publication
full work available at URL: 0022-1236(92)90013-9
OpenAlex ID: W2047972270
cites work: The Kauffman polynomial of links and representation theory
cites work: Entropy for Canonical Shifts
cites work: Q3719303
cites work: Entropy for automorphisms of \(II_1\) von Neumann algebras
cites work: Embeddings of U(1)-current algebras in non-commutative algebras of classical statistical mechanics
cites work: Superselection sectors with braid group statistics and exchange algebras
cites work: Braided compact closed categories with applications to low dimensional topology
cites work: Q4693152
cites work: INTRODUCTION TO THE YANG-BAXTER EQUATION
cites work: Index for subfactors
cites work: Hecke algebra representations of braid groups and link polynomials
cites work: Minimum index for subfactors and entropy. II
cites work: Characterization of crossed product (properly infinite case)
cites work: A remark on the minimal index of subgfactors
cites work: Index of subfactors and statistics of quantum fields. I
cites work: Index of subfactors and statistics of quantum fields. II: Correspondences, braid group statistics and Jones polynomial
cites work: Simple injective subfactors
cites work: Conformal field algebras with quantum symmetry from the theory of superselection sectors
cites work: Entropy and index for subfactors
cites work: Markov traces on universal Jones algebras and subfactors of finite index
cites work: Space-time fields and exchange fields
cites work: Hecke algebras of type \(A_ n\) and subfactors
cites work: Quantum groups and subfactors of type B, C, and D
cites work: Q3759378
cites work: Application of fusion rules to classification of subfactors
description: scientific article; zbMATH DE number 152023