Quantum Groups, Quantum Categories and Quantum Field Theory: 1542 - Brossura

Förhlich, Jürg

Brossura

ISBN 10: 3540566236 ISBN 13: 9783540566236

Casa editrice: Springer, 2009

Riassunto

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.

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Contenuti

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.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2009
• Lingua: Inglese
• ISBN 10: 3540566236
• ISBN 13: 9783540566236
• Rilegatura: Copertina flessibile
• Numero di pagine: 440
• Contatto del produttore: non disponibile
• Persona responsabile: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Germania