The Classification of Subfactors with Index at Most 5 Frac {1}{4} / Narjess Afzaly, Scott Morrison, and David Penneys.

Format:

Book

Author/Creator:

Afzaly, Narjess, author.

Morrison, Scott (Scott Edward), author.

Penneys, David, author.

Series:

Memoirs of the American Mathematical Society ; Volume 284.

Memoirs of the American Mathematical Society Series ; Volume 284

Language:

English

Subjects (All):

Algebraic varieties--Classification theory.

Algebraic varieties.

Categories (Mathematics).

Combinatorial enumeration problems.

Cyclotomy.

Factors (Algebra).

Index theory (Mathematics).

Physical Description:

1 online resource (94 pages)

Edition:

First edition.

Place of Publication:

Providence, RI : American Mathematical Society, [2023]

Summary:

"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.

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.

Notes:

Includes bibliographical references.

Description based on print version record.

ISBN:

9781470474430

1470474433