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• catalog abstract "This book reviews recent results on low-dimensional 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 semi-simple quotient thereof, a classfication of braided tensor categories generated by an object of q-dimension 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.".
• catalog contributor b4657397.
• catalog contributor b4657398.
• catalog created "c1993.".
• catalog date "1993".
• catalog date "c1993.".
• catalog dateCopyrighted "c1993.".
• catalog description "1. Introduction and Survey of Results -- 2. Local Quantum Theory with Braid Group Statistics. 2.1. Some Aspects of Low-Dimensional, 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].".
• catalog description "5.2. The Irreducible and Unitary Representations of [actual symbol not reproducible]. 5.3. Decomposition of Tensor Product Representations. 5.4. Fusion Rules, and q-Dimensions: 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.".
• catalog description "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. Non-bicolorable, finite graphs. A.4. Non-bicolorable, 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.".
• catalog description "Includes bibliographical references (p. 422-428) and index.".
• catalog description "This book reviews recent results on low-dimensional 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 semi-simple quotient thereof, a classfication of braided tensor categories generated by an object of q-dimension 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.".
• catalog extent "vii, 431 p. :".
• catalog hasFormat "Quantum groups, quantum categories, and quantum field theory.".
• catalog identifier "0387566236 (New York : acid-free)".
• catalog identifier "3540566236 (Berlin : acid-free) :".
• catalog isFormatOf "Quantum groups, quantum categories, and quantum field theory.".
• catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1542.".
• catalog isPartOf "Lecture notes in mathematics ; 1542".
• catalog issued "1993".
• catalog issued "c1993.".
• catalog language "eng".
• catalog publisher "Berlin : New York : Springer-Verlag,".
• catalog relation "Quantum groups, quantum categories, and quantum field theory.".
• catalog subject "530.1/43 20".
• catalog subject "Global analysis (Mathematics).".
• catalog subject "Group theory.".
• catalog subject "K-theory.".
• catalog subject "Mathematics.".
• catalog subject "QC20.7.G76 F76 1993".
• catalog subject "Quantum computing.".
• catalog subject "Quantum field theory.".
• catalog subject "Quantum groups.".
• catalog subject "Quantum theory.".
• catalog tableOfContents "1. Introduction and Survey of Results -- 2. Local Quantum Theory with Braid Group Statistics. 2.1. Some Aspects of Low-Dimensional, 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].".
• catalog tableOfContents "5.2. The Irreducible and Unitary Representations of [actual symbol not reproducible]. 5.3. Decomposition of Tensor Product Representations. 5.4. Fusion Rules, and q-Dimensions: 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.".
• catalog tableOfContents "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. Non-bicolorable, finite graphs. A.4. Non-bicolorable, 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.".
• catalog title "Quantum groups, quantum categories, and quantum field theory / Jürg Fröhlich, [Thomas Kerler].".
• catalog type "text".