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.
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ISBN-13
978-3-540-47611-5 (9783540476115)
DOI
Schweitzer Klassifikation
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.
