The Resource Quantum groups, quantum categories, and quantum field theory, Jürg Fröhlich, [Thomas Kerler]
Quantum groups, quantum categories, and quantum field theory, Jürg Fröhlich, [Thomas Kerler]
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The item Quantum groups, quantum categories, and quantum field theory, Jürg Fröhlich, [Thomas Kerler] represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Quantum groups, quantum categories, and quantum field theory, Jürg Fröhlich, [Thomas Kerler] represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 This book reviews recent results on lowdimensional quantum field theories and their connection with quantum group theory and the theory of braided, balanced tensor categories. It presents detailed, mathematically precise introductions to these subjects and then continues with new results. Among the main results are a detailed analysis of the representation theory of U (sl), for q a primitive root of unity, and a semisimple quotient thereof, a classfication of braided tensor categories generated by an object of qdimension less than two, and an application of these results to the theory of sectors in algebraic quantum field theory. This clarifies the notion of "quantized symmetries" in quantum fieldtheory. The reader is expected to be familiar with basic notions and resultsin algebra. The book is intended for research mathematicians, mathematical physicists and graduate students
 Language
 eng
 Extent
 1 online resource (vii, 431 pages)
 Contents

 1. Introduction and Survey of Results  2. Local Quantum Theory with Braid Group Statistics. 2.1. Some Aspects of LowDimensional, Local Quantum Field Theory. 2.2. Generalities Concerning Algebraic Field Theory. 2.3. Statistics and Fusion of Intertwiners; Statistical Dimensions. 2.4. Unitary Representations of the Braid Groups Derived from Local Quantum Theory; Markov Traces  3. Superselection Sectors and the Structure of Fusion Rule Algebras. 3.1. Definition of and General Relations in Fusion Rule Algebras and their Appearance in Local Quantum Field Theories. 3.2. Structure Theory for Fusion Rule Algebras. 3.3. Grading Reduction with Automorphisms and Normality Constraints in Fusion Rule Algebras. 3.4. Fusionrules with a Generator of Dimension not Greater than Two  4. Hopf Algebras and Quantum Groups at Roots of Unity  5. Representation Theory of [actual symbol not reproducible]. 5.1. Highest Weight Representations of [actual symbol not reproducible]
 5.2. The Irreducible and Unitary Representations of [actual symbol not reproducible]. 5.3. Decomposition of Tensor Product Representations. 5.4. Fusion Rules, and qDimensions: Selecting a List of Physical Representations  6. Path Representations of the Braid Groups for Quantum Groups at Roots of Unity. 6.1. Quotients of Representation Categories. 6.2. Braid Group Representations and Fusion Equations. 6.3. Unitarity of Braid Group Representations Obtained from U[subscript q](sl[subscript d + 1]). 6.4. Markov Traces  7. Duality Theory for Local Quantum Theories, Dimensions and Balancing in Quantum Categories. 7.1. General Definitions, Towers of Algebras. 7.2. Quantum Group Symmetries of Charged Fields. 7.3. The Index and Fundamental Decompositions. 7.4. Balancing Phases. 7.5. Theta  Categories  8. The Quantum Categories with a Generator of Dimension less than Two. 8.1. Product Categories and Induced Categories. 8.2. The A[subscript n]  Categories and Main Results
 A: Undirected Graphs with Norm not Larger than Two. A.1. Bicolorable, finite graphs. A.2. Bicolorable, infinite graphs (corresponding to N = [actual symbol not reproducible]). A.3. Nonbicolorable, finite graphs. A.4. Nonbicolorable, infinite graphs (N = [actual symbol not reproducible]). A.5. The higher graded fusionrule algebras  B: Fusion Rule Algebra Homomorphisms. B.1. [actual symbol not reproducible]. B.2. [actual symbol not reproducible]. B.3. [actual symbol not reproducible]. B.4. [actual symbol not reproducible]  Bibliography  Index
 Isbn
 9783540476115
 Label
 Quantum groups, quantum categories, and quantum field theory
 Title
 Quantum groups, quantum categories, and quantum field theory
 Statement of responsibility
 Jürg Fröhlich, [Thomas Kerler]
 Language
 eng
 Summary
 This book reviews recent results on lowdimensional quantum field theories and their connection with quantum group theory and the theory of braided, balanced tensor categories. It presents detailed, mathematically precise introductions to these subjects and then continues with new results. Among the main results are a detailed analysis of the representation theory of U (sl), for q a primitive root of unity, and a semisimple quotient thereof, a classfication of braided tensor categories generated by an object of qdimension less than two, and an application of these results to the theory of sectors in algebraic quantum field theory. This clarifies the notion of "quantized symmetries" in quantum fieldtheory. The reader is expected to be familiar with basic notions and resultsin algebra. The book is intended for research mathematicians, mathematical physicists and graduate students
 Action
 digitized
 Cataloging source
 SPLNM
 http://library.link/vocab/creatorName
 Fröhlich, Jürg
 Dewey number
 530.1/43
 Illustrations
 illustrations
 Index
 index present
 LC call number

 QC20.7.G76
 QA3
 LC item number

 F76 1993
 .L28 no. 1542
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorDate
 1965
 http://library.link/vocab/relatedWorkOrContributorName
 Kerler, Thomas
 Series statement
 Lecture notes in mathematics,
 Series volume
 1542
 http://library.link/vocab/subjectName

 Quantum groups
 Quantum field theory
 Quantum field theory
 Quantum groups
 Kwantumveldentheorie
 Quantengruppe
 Quantenfeldtheorie
 Kategorientheorie
 Label
 Quantum groups, quantum categories, and quantum field theory, Jürg Fröhlich, [Thomas Kerler]
 Bibliography note
 Includes bibliographical references (pages 422428) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 1. Introduction and Survey of Results  2. Local Quantum Theory with Braid Group Statistics. 2.1. Some Aspects of LowDimensional, Local Quantum Field Theory. 2.2. Generalities Concerning Algebraic Field Theory. 2.3. Statistics and Fusion of Intertwiners; Statistical Dimensions. 2.4. Unitary Representations of the Braid Groups Derived from Local Quantum Theory; Markov Traces  3. Superselection Sectors and the Structure of Fusion Rule Algebras. 3.1. Definition of and General Relations in Fusion Rule Algebras and their Appearance in Local Quantum Field Theories. 3.2. Structure Theory for Fusion Rule Algebras. 3.3. Grading Reduction with Automorphisms and Normality Constraints in Fusion Rule Algebras. 3.4. Fusionrules with a Generator of Dimension not Greater than Two  4. Hopf Algebras and Quantum Groups at Roots of Unity  5. Representation Theory of [actual symbol not reproducible]. 5.1. Highest Weight Representations of [actual symbol not reproducible]
 5.2. The Irreducible and Unitary Representations of [actual symbol not reproducible]. 5.3. Decomposition of Tensor Product Representations. 5.4. Fusion Rules, and qDimensions: Selecting a List of Physical Representations  6. Path Representations of the Braid Groups for Quantum Groups at Roots of Unity. 6.1. Quotients of Representation Categories. 6.2. Braid Group Representations and Fusion Equations. 6.3. Unitarity of Braid Group Representations Obtained from U[subscript q](sl[subscript d + 1]). 6.4. Markov Traces  7. Duality Theory for Local Quantum Theories, Dimensions and Balancing in Quantum Categories. 7.1. General Definitions, Towers of Algebras. 7.2. Quantum Group Symmetries of Charged Fields. 7.3. The Index and Fundamental Decompositions. 7.4. Balancing Phases. 7.5. Theta  Categories  8. The Quantum Categories with a Generator of Dimension less than Two. 8.1. Product Categories and Induced Categories. 8.2. The A[subscript n]  Categories and Main Results
 A: Undirected Graphs with Norm not Larger than Two. A.1. Bicolorable, finite graphs. A.2. Bicolorable, infinite graphs (corresponding to N = [actual symbol not reproducible]). A.3. Nonbicolorable, finite graphs. A.4. Nonbicolorable, infinite graphs (N = [actual symbol not reproducible]). A.5. The higher graded fusionrule algebras  B: Fusion Rule Algebra Homomorphisms. B.1. [actual symbol not reproducible]. B.2. [actual symbol not reproducible]. B.3. [actual symbol not reproducible]. B.4. [actual symbol not reproducible]  Bibliography  Index
 Control code
 298692436
 Dimensions
 unknown
 Extent
 1 online resource (vii, 431 pages)
 Form of item
 online
 Isbn
 9783540476115
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 illustrations.
 Reproduction note
 Electronic reproduction.
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)298692436
 System details
 Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
 Label
 Quantum groups, quantum categories, and quantum field theory, Jürg Fröhlich, [Thomas Kerler]
 Bibliography note
 Includes bibliographical references (pages 422428) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 1. Introduction and Survey of Results  2. Local Quantum Theory with Braid Group Statistics. 2.1. Some Aspects of LowDimensional, Local Quantum Field Theory. 2.2. Generalities Concerning Algebraic Field Theory. 2.3. Statistics and Fusion of Intertwiners; Statistical Dimensions. 2.4. Unitary Representations of the Braid Groups Derived from Local Quantum Theory; Markov Traces  3. Superselection Sectors and the Structure of Fusion Rule Algebras. 3.1. Definition of and General Relations in Fusion Rule Algebras and their Appearance in Local Quantum Field Theories. 3.2. Structure Theory for Fusion Rule Algebras. 3.3. Grading Reduction with Automorphisms and Normality Constraints in Fusion Rule Algebras. 3.4. Fusionrules with a Generator of Dimension not Greater than Two  4. Hopf Algebras and Quantum Groups at Roots of Unity  5. Representation Theory of [actual symbol not reproducible]. 5.1. Highest Weight Representations of [actual symbol not reproducible]
 5.2. The Irreducible and Unitary Representations of [actual symbol not reproducible]. 5.3. Decomposition of Tensor Product Representations. 5.4. Fusion Rules, and qDimensions: Selecting a List of Physical Representations  6. Path Representations of the Braid Groups for Quantum Groups at Roots of Unity. 6.1. Quotients of Representation Categories. 6.2. Braid Group Representations and Fusion Equations. 6.3. Unitarity of Braid Group Representations Obtained from U[subscript q](sl[subscript d + 1]). 6.4. Markov Traces  7. Duality Theory for Local Quantum Theories, Dimensions and Balancing in Quantum Categories. 7.1. General Definitions, Towers of Algebras. 7.2. Quantum Group Symmetries of Charged Fields. 7.3. The Index and Fundamental Decompositions. 7.4. Balancing Phases. 7.5. Theta  Categories  8. The Quantum Categories with a Generator of Dimension less than Two. 8.1. Product Categories and Induced Categories. 8.2. The A[subscript n]  Categories and Main Results
 A: Undirected Graphs with Norm not Larger than Two. A.1. Bicolorable, finite graphs. A.2. Bicolorable, infinite graphs (corresponding to N = [actual symbol not reproducible]). A.3. Nonbicolorable, finite graphs. A.4. Nonbicolorable, infinite graphs (N = [actual symbol not reproducible]). A.5. The higher graded fusionrule algebras  B: Fusion Rule Algebra Homomorphisms. B.1. [actual symbol not reproducible]. B.2. [actual symbol not reproducible]. B.3. [actual symbol not reproducible]. B.4. [actual symbol not reproducible]  Bibliography  Index
 Control code
 298692436
 Dimensions
 unknown
 Extent
 1 online resource (vii, 431 pages)
 Form of item
 online
 Isbn
 9783540476115
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 illustrations.
 Reproduction note
 Electronic reproduction.
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)298692436
 System details
 Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
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