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Tensor categories and endomorphisms of Von Neumann algebras [electronic resource] : with applications to quantum field theory / Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo, Karl-Henning Rehren.

Bischoff, Marcel, author.; Kawahigashi, Yasuyuki, author.; Longo, Roberto, author.; Rehren, Karl-Henning, author.
2015
QA433
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Title
Tensor categories and endomorphisms of Von Neumann algebras [electronic resource] : with applications to quantum field theory / Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo, Karl-Henning Rehren.
ISBN
9783319143019 electronic book
3319143018 electronic book
9783319143002
DOI
https://doi.org/10.1007/978-3-319-14301-9
Published
Cham : Springer, 2015.
Language
English
Description
1 online resource (x, 94 pages) : illustrations.
Item Number
10.1007/978-3-319-14301-9 doi
Call Number
QA433
Dewey Decimal Classification
515/.63
Summary
C* tensor categories are a point of contact where Operator Algebras and Quantum Field Theory meet. They are the underlying unifying concept for homomorphisms of (properly infinite) von Neumann algebras and representations of quantum observables. The present introductory text reviews the basic notions and their cross-relations in different contexts. The focus is on Q-systems that serve as complete invariants, both for subfactors and for extensions of quantum field theory models. It proceeds with various operations on Q-systems (several decompositions, the mirror Q-system, braided product, centre and full centre of Q-systems) some of which are defined only in the presence of a braiding. The last chapter gives a brief exposition of the relevance of the mathematical structures presented in the main body for applications in Quantum Field Theory (in particular two-dimensional Conformal Field Theory, also with boundaries or defects).
Bibliography, etc. Note
Includes bibliographical references.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed January 30, 2015).
Added Author
Bischoff, Marcel, author.
Kawahigashi, Yasuyuki, author.
Longo, Roberto, author.
Rehren, Karl-Henning, author.
Series
SpringerBriefs in mathematical physics ; volume 3.
Available in Other Form
Print version: 9783319143002
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Introduction
Homomorphisms of von Neumann algebras
Endomorphisms of infinite factors
Homomorphisms and subfactors
Non-factorial extensions
Frobenius algebras, Q-systems and modules
C* Frobenius algebras
Q-systems and extensions
The canonical Q-system
Modules of Q-systems
Induced Q-systems and Morita equivalence
Bimodules
Tensor product of bimodules
Q-system calculus
Reduced Q-systems
Central decomposition of Q-systems
Irreducible decomposition of Q-systems
Intermediate Q-systems
Q-systems in braided tensor categories
a-induction
Mirror Q-systems
Centre of Q-systems
Braided product of Q-systems
The full centre
Modular tensor categories
The braided product of two full centres
Applications in QFT
Basics of algebraic quantum field theory
Hard boundaries
Transparent boundaries
Further directions
Conclusions.

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