Quantum Groups, Quantum Categories and Quantum Field Theory / by Jürg Fröhlich, Thomas Kerler.

Format:

Book

Author/Creator:

Fröhlich, Jürg, author.

Kerler, Thomas, 1965- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1542.

Lecture Notes in Mathematics, 0075-8434 ; 1542

Language:

English

Subjects (All):

K-theory.

Group theory.

Global analysis (Mathematics).

Quantum theory.

K-Theory.

Group Theory and Generalizations.

Analysis.

Quantum Information Technology, Spintronics.

Quantum Physics.

Local Subjects:

K-Theory.

Group Theory and Generalizations.

Analysis.

Quantum Information Technology, Spintronics.

Quantum Physics.

Physical Description:

1 online resource (VIII, 432 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1993.

System Details:

text file PDF

Summary:

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:

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.

Other Format:

Printed edition:

ISBN:

9783540476115

Access Restriction:

Restricted for use by site license.