| Lectures on Algebraic Quantum Groups 2002 Edition Contributor(s): Brown, Ken (Author), Goodearl, Ken R. (Author) |
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ISBN: 3764367148 ISBN-13: 9783764367145 Publisher: Birkhauser OUR PRICE: $52.20 Product Type: Paperback Published: April 2002 Annotation: This book consists of an expanded set of lectures on algebraic aspects of quantum groups, concentrating particularly on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras. The approach, a mixture of introductory textbook, lecture notes, and overview survey, is designed to allow access by graduate students and by researchers new to the areas, as well as by experts, and to provide a basis for further study of the subject. Thus, large parts of the material are developed in full textbook style, with many examples and numerous exercises; other portions are discussed with sketches of proofs, while still other material is quoted without proof. Much associated background material is outlined in a series of appendices. Among the topics covered for the first time in book form are a discussion of the nature of the prime spectrum of a "generic" quantum algebra, and details of how the Hopf algebra structure of the algebra and the Poisson algebra structure of the centre carry important consequences for quantized algebras when the quantum parameter is a root of unity. The book is structured in three parts: one introductory part with many examples plus background material, one concentrating on generic quantized coordinate rings, and one dealing with quantized algebras at roots of unity. |
| Additional Information |
| BISAC Categories: - Mathematics | Group Theory - Mathematics | Algebra - Abstract - Mathematics | Topology - General |
| Dewey: 512 |
| LCCN: 2006295657 |
| Series: Advanced Courses in Mathematics: CRM Barcelona |
| Physical Information: 0.75" H x 7" W x 10" (1.39 lbs) 348 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: In September 2000, at the Centre de Recerca Matematica in Barcelona, we pre- sented a 30-hour Advanced Course on Algebraic Quantum Groups. After the course, we expanded and smoothed out the material presented in the lectures and inte- grated it with the background material that we had prepared for the participants; this volume is the result. As our title implies, our aim in the course and in this text is to treat selected algebraic aspects of the subject of quantum groups. Sev- eral of the words in the previous sentence call for some elaboration. First, we mean to convey several points by the term 'algebraic' - that we are concerned with algebraic objects, the quantized analogues of 'classical' algebraic objects (in contrast, for example, to quantized versions of continuous function algebras on compact groups); that we are interested in algebraic aspects of the structure of these objects and their representations (in contrast, for example, to applications to other areas of mathematics); and that our tools will be drawn primarily from noncommutative algebra, representation theory, and algebraic geometry. Second, the term 'quantum groups' itself. This label is attached to a large and rapidly diversifying field of mathematics and mathematical physics, originally launched by developments around 1980 in theoretical physics and statistical me- chanics. It is a field driven much more by examples than by axioms, and so resists attempts at concise description (but see Chapter 1. 1 and the references therein). |
