Foundations of Quantum Group Theory

ISBN-13: 9780521648684 / Angielski / Miękka / 2000 / 664 str.

Shahn Majid

Opis

This is a graduate-level text that systematically develops the foundations of the subject. Quantum groups (i.e. Hopf algebras) are treated as mathematical objects in their own right; basic properties and theorems are proven in detail from this standpoint, including the results underlying key applications. 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. The explicit proofs and a great many worked examples and exercises will allow readers to quickly pick up the techniques needed for working in this exciting new field.

Recenzje

'… 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, Bulletin of the London Mathematical Society

Spis treści

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.