Quantum Groups, Quantum Categories and Quantum Field Theory
Published on 12. May 1993
Book
Paperback/Softback
VIII, 432 pages
978-3-540-56623-6 (ISBN)
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.
More details
Series
Edition
1st ed. 1993. 2nd printing 1995
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
VIII, 432 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 24 mm
Weight
663 gr
ISBN-13
978-3-540-56623-6 (9783540566236)
DOI
10.1007/BFb0084244
Schweitzer Classification
Content
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.