Memoirs of the American Mathematical Society Series ; Volume 284 [More in this series]
Summary note
"Subfactor standard invariants encode quantum symmetries. The small index subfactor classification program has been a rich source of interesting quantum symmetries. We give the complete classification of subfactor standard invariants to index 5 1/4 , which includes 3 [plus] [sqaure root]5, the first interesting composite index"-- Provided by publisher.
Bibliographic references
Includes bibliographical references.
Source of description
Description based on print version record.
Contents
Cover
Title page
Chapter 1. Introduction
1.1. Quantum symmetries and the Galois correspondence
Acknowledgments
Chapter 2. Background
2.1. Subfactors and their standard invariants
2.2. Towards classification
2.3. Some first obstructions
Chapter 3. The main theorem
3.1. The future
3.2. Proof of the main theorem
Chapter 4. Better combinatorics for graph enumeration
4.1. Generation by canonical construction paths for principal graphs
4.2. Exhaustivity and uniqueness
4.3. The implementations
4.4. Application to graph pairs up to index 51/4
Chapter 5. Weeds with branch factor =1
5.1. The remaining =1 weed
5.2. Relative dimensions and doubly one-by-one connection entries
5.3. A variation on Calegari-Guo
5.4. The tail enumerator and periodicity
5.5. Ruling out the infinite depth graph
Chapter 6. Ruling out weeds using branch factor inequalities
6.1. Ruling out a particular *11 weed
6.2. Ruling out the remaining *11 weeds
6.3. Ruling out two particular *10 weeds with doubly one-by-ones
6.3.1. A truncation of ℱ from [MPPS12]
6.3.2. Another *10 weed with undetermined relative dimensions
6.4. Ruling out the remaining *10 weeds
6.5. Ruling out a graph with formal codegrees
Chapter 7. Ruling out 4-spokes
Chapter 8. Cyclotomicity of vines
Appendix A. Appendices
A.1. Cyclotomicity bounds
A.2. The fusion ring of
A.3. Subfactors with index in (4,51/4]
A.4. The map of subfactors
Bibliography
Back Cover.
ISBN
1-4704-7443-3
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