Foundations of Quantum Group Theory

by Shahn Majid

Overview

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.

Product Details

ISBN-13:	9780521648684
Publisher:	Cambridge University Press
Publication date:	04/13/2000
Edition description:	1 PBK ED
Pages:	664
Product dimensions:	6.85(w) x 9.72(h) x 1.61(d)

Table of Contents

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.

Editorial Reviews

"...this is a remarkable book, written in a rigorous style (all necessary statements are proved explicitly) by an acknowledged leader in the field." Dmitrii I. Gurevich, Mathematical Reviews

From the Publisher

This graduate level textbook for theoretical physicists and mathematicians covers Hopf algebras, 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 -deformed physics. Originally published in 1995, this is a corrected, paperback edition. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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