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Field name	Details
Dewey Class	512.66
Title	Quantum Groups, Quantum Categories and Quantum Field Theory ([EBook]) / by Jürg Fröhlich, Thomas Kerler.
Author	Fröhlich, Jürg
Added Personal Name	Kerler, Thomas. , 1965-
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 1993.
Physical Details	VIII, 432 pages : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1542
ISBN	9783540476115
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/BFb0084244
Links to Related Works	Subject References: Analysis (Mathematics) . Group theory . Group Theory and Generalizations . K-Theory . Mathematical analysis . Quantum computers . Quantum Information Technology, Spintronics . Quantum Physics . Spintronics . Authors: author . Fröhlich, Jürg . Kerler, Thomas. 1965- . Kerler, Thomas, 1965- . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 512.66 .

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Quantum Groups, Quantum Categories and Quantum Field Theory

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