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Fusion of Defects. (Record no. 10468)

MARC details
000 -LEADER
fixed length control field 05501nam a22005053i 4500
001 - CONTROL NUMBER
control field EBC5770282
003 - CONTROL NUMBER IDENTIFIER
control field MiAaPQ
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20240724113715.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS
fixed length control field m o d |
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr cnu||||||||
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 240724s2019 xx o ||||0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781470450656
Qualifying information (electronic bk.)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Canceled/invalid ISBN 9781470435233
035 ## - SYSTEM CONTROL NUMBER
System control number (MiAaPQ)EBC5770282
035 ## - SYSTEM CONTROL NUMBER
System control number (Au-PeEL)EBL5770282
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)1096290603
040 ## - CATALOGING SOURCE
Original cataloging agency MiAaPQ
Language of cataloging eng
Description conventions rda
-- pn
Transcribing agency MiAaPQ
Modifying agency MiAaPQ
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA611 .B378 2019
082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 530.14/3
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Bartels, Arthur.
245 10 - TITLE STATEMENT
Title Fusion of Defects.
250 ## - EDITION STATEMENT
Edition statement 1st ed.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture Providence :
Name of producer, publisher, distributor, manufacturer American Mathematical Society,
Date of production, publication, distribution, manufacture, or copyright notice 2019.
264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Date of production, publication, distribution, manufacture, or copyright notice ©2019.
300 ## - PHYSICAL DESCRIPTION
Extent 1 online resource (114 pages)
336 ## - CONTENT TYPE
Content type term text
Content type code txt
Source rdacontent
337 ## - MEDIA TYPE
Media type term computer
Media type code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier type term online resource
Carrier type code cr
Source rdacarrier
490 1# - SERIES STATEMENT
Series statement Memoirs of the American Mathematical Society Series ;
Volume/sequential designation v.258
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Cover -- Title page -- Acknowledgments -- Introduction -- OT1OT1cmrcmrmmnnnsca. Conformal nets -- OT1OT1cmrcmrmmnnnscb. Defects -- OT1OT1cmrcmrmmnnnscc. Sectors -- OT1OT1cmrcmrmmnnnscd. The vacuum sector of a defect -- OT1OT1cmrcmrmmnnnsce. Composition of defects -- OT1OT1cmrcmrmmnnnscf. Fusion of sectors and the interchange isomorphism -- OT1OT1cmrcmrmmnnnscg. The 1⊠1-isomorphism -- OT1OT1cmrcmrmmnnnsch. Construction of the 1⊠1-isomorphism -- Chapter 1. Defects -- 1.OT1OT1cmrcmrmmnnnsca. Bicolored intervals and circles -- 1.OT1OT1cmrcmrmmnnnscb. Definition of defects -- 1.OT1OT1cmrcmrmmnnnscc. Examples of defects -- 1.OT1OT1cmrcmrmmnnnscd. The category \CN₁ of defects -- 1.OT1OT1cmrcmrmmnnnsce. Composition of defects -- 1.OT1OT1cmrcmrmmnnnscf. Associativity of composition -- Chapter 2. Sectors -- 2.OT1OT1cmrcmrmmnnnsca. The category \CN₂ of sectors -- 2.OT1OT1cmrcmrmmnnnscb. Horizontal fusion -- 2.OT1OT1cmrcmrmmnnnscc. Vertical fusion -- Chapter 3. Properties of the composition of defects -- 3.OT1OT1cmrcmrmmnnnsca. Left and right units -- 3.OT1OT1cmrcmrmmnnnscb. Semisimplicity of the composite defect -- Chapter 4. A variant of horizontal fusion -- 4.OT1OT1cmrcmrmmnnnsca. The keyhole and keystone fusion -- 4.OT1OT1cmrcmrmmnnnscb. The keyhole fusion of vacuum sectors of defects -- 4.OT1OT1cmrcmrmmnnnscc. The keystone fusion of vacuum sectors of defects -- 4.OT1OT1cmrcmrmmnnnscd. Comparison between fusion and keystone fusion -- Chapter 5. Haag duality for composition of defects -- 5.OT1OT1cmrcmrmmnnnsca. The dimension of the Haag inclusion -- 5.OT1OT1cmrcmrmmnnnscb. The double bridge algebra is a factor -- 5.OT1OT1cmrcmrmmnnnscc. The dimension of the bridge inclusions -- Chapter 6. The 1⊠1-isomorphism -- 6.OT1OT1cmrcmrmmnnnsca. The 1⊠1-map is an isomorphism -- 6.OT1OT1cmrcmrmmnnnscb. The 1⊠1-isomorphism for an identity defect.
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 6.OT1OT1cmrcmrmmnnnscc. Unitors for horizontal fusion of sectors -- 6.OT1OT1cmrcmrmmnnnscd. The interchange isomorphism -- Appendix A. Components for the 3-category of conformal nets -- Appendix B. Von Neumann algebras -- B.I. The Haagerup ²-space -- B.II. Connes fusion -- B.III. Cyclic fusion -- B.IV. Fusion and fiber product of von Neumann algebras -- B.V. Compatibility with tensor products -- B.VI. Dualizability -- B.VII. Statistical dimension and minimal index -- B.VIII. Functors between module categories -- B.IX. The split property -- B.X. Two-sided fusion on ²-spaces -- Appendix C. Conformal nets -- C.I. Axioms for conformal nets -- C.II. The vacuum sector -- C.III. Gluing vacuum sectors -- C.IV. Finite-index conformal nets -- C.V. Sectors and the Hilbert space of the annulus -- C.VI. Extension of conformal nets to all 1-manifolds -- Appendix D. Diagram of dependencies -- Bibliography -- Back Cover.
520 ## - SUMMARY, ETC.
Summary, etc. Conformal nets provide a mathematical model for conformal field theory. The authors define a notion of defect between conformal nets, formalizing the idea of an interaction between two conformal field theories. They introduce an operation of fusion of defects, and prove that the fusion of two defects is again a defect, provided the fusion occurs over a conformal net of finite index. There is a notion of sector (or bimodule) between two defects, and operations of horizontal and vertical fusion of such sectors. The authors' most difficult technical result is that the horizontal fusion of the vacuum sectors of two defects is isomorphic to the vacuum sector of the fused defect. Equipped with this isomorphism, they construct the basic interchange isomorphism between the horizontal fusion of two vertical fusions and the vertical fusion of two horizontal fusions of sectors.
588 ## - SOURCE OF DESCRIPTION NOTE
Source of description note Description based on publisher supplied metadata and other sources.
590 ## - LOCAL NOTE (RLIN)
Local note Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Topological fields.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Generalized spaces.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Topology.
655 #4 - INDEX TERM--GENRE/FORM
Genre/form data or focus term Electronic books.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Douglas, Christopher.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Henriques, André.
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Print version:
Main entry heading Bartels, Arthur
Title Fusion of Defects
Place, publisher, and date of publication Providence : American Mathematical Society,c2019
International Standard Book Number 9781470435233
797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN)
Corporate name or jurisdiction name as entry element ProQuest (Firm)
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Memoirs of the American Mathematical Society Series
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5770282">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5770282</a>
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