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Tensor categories and endomorphisms ...

Bischoff, Marcel.

Tensor categories and endomorphisms of Von Neumann algebraswith applications to quantum field theory /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Tensor categories and endomorphisms of Von Neumann algebrasby Marcel Bischoff ... [et al.].
Reminder of title:	with applications to quantum field theory /
other author:	Bischoff, Marcel.
Published:	Cham :Springer International Publishing :2015.
Description:	x, 94 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Calculus of tensors.
Online resource:	http://dx.doi.org/10.1007/978-3-319-14301-9
ISBN:	9783319143019 (electronic bk.)

Tensor categories and endomorphisms of Von Neumann algebraswith applications to quantum field theory /
Tensor categories and endomorphisms of Von Neumann algebraswith applications to quantum field theory /[electronic resource] :by Marcel Bischoff ... [et al.]. - Cham :Springer International Publishing :2015. - x, 94 p. :ill., digital ;24 cm. - SpringerBriefs in mathematical physics,v.32197-1757 ;. - SpringerBriefs in mathematical physics ;v.1..

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.

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).

ISBN: 9783319143019 (electronic bk.)

Standard No.: 10.1007/978-3-319-14301-9doiSubjects--Topical Terms:

210256
Calculus of tensors.

LC Class. No.: QA433

Dewey Class. No.: 515.63

Tensor categories and endomorphisms of Von Neumann algebraswith applications to quantum field theory /
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245 0 0 $a Tensor categories and endomorphisms of Von Neumann algebras $h [electronic resource] : $b with applications to quantum field theory / $c by Marcel Bischoff ... [et al.].
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a x, 94 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematical physics, $x 2197-1757 ; $v v.3
505 0 $a 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.
520 $a 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).
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