Foundations of Quantum Group Theory
Cambridge University Press
Edition: New Ed, 8/21/2008
EAN 9780521648684, ISBN10: 0521648688
Paperback, 664 pages, 24.4 x 17 x 3.3 cm
Language: English
Originally published in English
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.
Introduction
1. Definition of Hopf algebras
2. Quasitriangular Hopf algebras
3. Quantum enveloping algebras
4. Matrix quantum groups
5. Quantum random walks and combinatorics
6. Bicrossproduct Hopf algebras
7. Quantum double and double cross products
8. Lie bialgebras and Poisson brackets
9. Representation theory
10. Braided groups and q-deformation
References
Symbols
Indexes.