Topological Quantum Field Theories from Subfactors: 1st Edition (Paperback) book cover

Topological Quantum Field Theories from Subfactors

1st Edition

By Vijay Kodiyalam, V.S. Sunder

Chapman and Hall/CRC

136 pages | 15 B/W Illus.

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Paperback: 9781584882411
pub: 2000-12-07
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Description

Pure mathematicians have only recently begun a rigorous study of topological quantum field theories (TQFTs). Ocneanu, in particular, showed that subfactors yield TQFTs that complement the Turaev-Viro construction. Until now, however, it has been difficult to find an account of this work that is both detailed and accessible.

Topological Quantum Field Theories from Subfactors provides a self-contained, explicit description of Ocneanu's construction It introduces and discusses its various ingredients with the distinct advantage of employing only genuine triangulations. The authors begin with axioms for a TQFT, go through the Turaev-Viro prescription for constructing such a TQFT, and finally work through Ocneanu's method of starting with a finite depth hyperfinite subfactor" and obtaining the data needed to invoke the Turaev-Viro machine.

The authors provide a very concise treatment of finite factors of type and their bimodules and include details and calculations for all constructions. They also present, perhaps for the first time in book form, notions such as quantization functors and fusion algebras. Accessible to graduate students and others just beginning to explore this intriguing topic, Topological Quantum Field Theories from Subfactors will also be of interest to researchers in both mathematics and theoretical physics.

Table of Contents

PRELIMINARIES ON TQFTs

Introduction

Quantizaiton Functors

Fusion Algebras

THE INVARIANT

The Construction

Invariance

von NEUMANN ALGEGRAS

Preliminaries on II1 Factors

Bases and M-Valued Inner Products

Contragredients and Tensor Products

Frobenius Reciprocity

TQFTs from Subfactors

THE GROUP EXAMPLE

The TQFT

The Quantum Double

APPENDIX

Some Topological Preliminaries

Simplicial Complexes

About the Series

Chapman & Hall/CRC Research Notes in Mathematics Series

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Subject Categories

BISAC Subject Codes/Headings:
MAT012000
MATHEMATICS / Geometry / General
MAT037000
MATHEMATICS / Functional Analysis
SCI040000
SCIENCE / Mathematical Physics