Tensor Categories and Endomorphisms of von Neumann Algebras with App
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 presen
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Marcel Bischoff Yasuyuki Kawahigashi Roberto Longo Karl-Henning Rehren
Tensor Categories and Endomorphisms of von Neumann Algebras with Applications to Quantum Field Theory
SpringerBriefs in Mathematical Physics Volume 3
Series editors Nathanaël Berestycki, Cambridge, UK Mihalis Dafermos, Cambridge, UK Tohru Eguchi, Tokyo, Japan Atsuo Kuniba, Tokyo, Japan Matilde Marcolli, Pasadena, USA Bruno Nachtergaele, Davis, USA
More information about this series at http://www.springer.com/series/11953
Marcel Bischoff Yasuyuki Kawahigashi Roberto Longo Karl-Henning Rehren •
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Tensor Categories and Endomorphisms of von Neumann Algebras with Applications to Quantum Field Theory
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Marcel Bischoff Institut für Theoretische Physik Universität Göttingen Göttingen Germany
Roberto Longo Dipartimento di Matematica Università di Roma “Tor Vergata” Rome Italy
Yasuyuki Kawahigashi Department of Mathematical Sciences and Kavli IPMU (WPI) The University of Tokyo Tokyo Japan
Karl-Henning Rehren Institut für Theoretische Physik Universität Göttingen Göttingen Germany
ISSN 2197-1757 ISSN 2197-1765 (electronic) SpringerBriefs in Mathematical Physics ISBN 978-3-319-14300-2 ISBN 978-3-319-14301-9 (eBook) DOI 10.1007/978-3-319-14301-9 Library of Congress Control Number: 2014958015 Springer Cham Heidelberg New York Dordrecht London © The Author(s) 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)
Preface
Subfactors (unital inclusions of von Neumann algebras with trivial centre) became a thriving focus of research interest after Vaughan Jones discovered in 1983 the quantization of the index below four. The associated principal graph was immediately identified as an important combinatorial invariant beyond the index, controlling the induction and restriction of bimodules of and between the two factors; more detailed information is encoded in the “plan
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