Details

Subject(s)

• Algebraic varieties—Classification theory [Browse]
• Categories (Mathematics) [Browse]
• Combinatorial enumeration problems [Browse]
• Cyclotomy [Browse]
• Factors (Algebra) [Browse]
• Index theory (Mathematics) [Browse]

Author

• Morrison, Scott (Scott Edward) [Browse]
• Penneys, David [Browse]

Series

• Memoirs of the American Mathematical Society ; Volume 284. [More in this series]
• 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.

Show 37 more Contents items

ISBN

1-4704-7443-3

Statement on language in description

Princeton University Library aims to describe library materials in a manner that is respectful to the individuals and communities who create, use, and are represented in the collections we manage. Read more...