Foundations of Quantum Group Theory

Shahn Majid

doi:10.1017/CBO9780511613104

Now in paperback, this is a graduate level text for theoretical physicists and mathematicians which systematically lays out the foundations for the subject of Quantum Groups in a clear and accessible way. The topic is developed in a logical manner with quantum groups (Hopf Algebras) treated as mathematical objects in their own right. After formal definitions and basic theory, the book goes on to cover such topics as quantum enveloping algebras, matrix quantum groups, combinatorics, cross products of various kinds, the quantum double, the semiclassical theory of Poisson-Lie groups, the representation theory, braided groups and applications to q-deformed physics. Explicit proofs and many examples will allow the reader quickly to pick up the techniques needed for working in this exciting new field.

‘… a coherent, detailed path through the field, with full, followable proofs and clear, readable explanations. It is a pleasure to follow this path with a guide who, unlike many mathematical authors, does not shirk his duty to write, and who shares with his readers his general understanding of and above all his enthusiasm for his subject.’

Tony Sudbery Source: Bulletin of the London Mathematical Society

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Foundations of Quantum Group Theory

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Contents

Frontmatter
pp i-vi

Contents
pp vii-x

Introduction
pp xi-xx

1 - Definition of Hopf algebras
pp 1-37

2 - Quasitriangular Hopf algebras
pp 38-71

3 - Quantum enveloping algebras
pp 72-107

4 - Matrix quantum groups
pp 108-177

5 - Quantum random walks and combinatorics
pp 178-222

6 - Bicrossproduct Hopf algebras
pp 223-301

7 - Quantum double and double cross products
pp 302-363

8 - Lie bialgebras and Poisson brackets
pp 364-435

9 - Representation theory
pp 436-526

10 - Braided groups and q-deformation
pp 527-610

References
pp 611-624

Symbols
pp 625-628

Index
pp 629-639

2-Index
pp 640-640

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