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Quantum Groups, Quantum Categories and Quantum Field Theory : Lecture Notes in Mathematics - Jurg Frohlich

Quantum Groups, Quantum Categories and Quantum Field Theory

Lecture Notes in Mathematics

Paperback Published: 1st February 1995
ISBN: 9783540566236
Number Of Pages: 432

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This book reviews recent results on low-dimensional quantumfield theories and their connection with quantum grouptheory and the theory of braided, balanced tensorcategories. It presents detailed, mathematically preciseintroductions to these subjects and then continues with newresults. Among the main results are a detailed analysis ofthe representation theory of U (sl ), for q a primitiveroot of unity, and a semi-simple quotient thereof, aclassfication of braided tensor categories generated by anobject of q-dimension less than two, and an application ofthese results to the theory of sectors in algebraic quantumfield theory. This clarifies the notion of "quantizedsymmetries" in quantum fieldtheory. The reader is expectedto be familiar with basic notions and resultsin algebra.The book is intended for research mathematicians,mathematical physicists and graduate students.

and survey of results.- Local quantum theory with braid group statistics.- Superselection sectors and the structure of fusion rule algebras.- Hopf algebras and quantum groups at roots of unity.- Representation theory of U q red (s? 2).- Path representations of the braid groups for quantum groups at roots of unity.- Duality theory for local quantum theories, dimensions and balancing in quantum categories.- The quantum categories with a generator of dimension less than two.

ISBN: 9783540566236
ISBN-10: 3540566236
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 432
Published: 1st February 1995
Publisher: SPRINGER VERLAG GMBH
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 2.26
Weight (kg): 0.61