Item description for Quantum Groups and Their Representations (Theoretical and Mathematical Physics) by A. U. Klimyk & Konrad Schmudgen...
This book provides a treatment of the theory of quantum groups (quantized universal enveloping algebras and quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The theory of the simplest and most important quantum groups and their representations is presented in detail. A number of topics and results from the more advanced general theory are developed and discussed. Many applications in mathematical and theoretical physics are indicated. The book starts as an introduction for the beginner and continues at a textbook level for graduate students in physics and in mathematics. It may serve as a reference for more advanced readers.
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Est. Packaging Dimensions: Length: 1.5" Width: 6.5" Height: 9.75" Weight: 2.1 lbs.
Release Date Jan 20, 1998
ISBN 3540634525 ISBN13 9783540634522
Reviews - What do customers think about Quantum Groups and Their Representations (Theoretical and Mathematical Physics)?
Very good introduction to, and reference on, Quantum Groups Jan 28, 2006
This is a very good and solid introduction to, and reference book on, quantum groups (or quantum algebras, as they are also known). It is one of the more clear volumes on the subject, and presents information in a fairly straightforward way.
As with many introductions to quantum groups, it can take a while to understand what is happening unless one already has some understanding of the field, however, the writing is not obtuse.
One of the notable aspects of it (for me) was that it clearly presents the differences between the Drinfeld-Jimbo version of the quantum group (defined over the ring of power series in an indeterminate) and Jimbo's version of the quantum group (defined over the complex field). The Drinfeld-Jimbo quantum group admits a universal R-matrix while the Jimbo version does not - for the latter, one can define solutions of the matrix Yang-Baxter equation from any integrable finite dimensional representation but this must be done carefully, and this volume presents this problem clearly.
I recommend this volume for graduate students working on quantum groups; I referred to it many times in my Ph.D studies, and also to people working with quantum groups.