Lectures on Algebraic Quantum Groups (Advanced Courses in Mathematics - CRM Barcelona)
Edition: 1 edition
Publisher: Birkhäuser Basel
Published: April 29, 2002
Language: eng
Format: Paperback
Number of pages: 348
ISBN-13: 9783764367145
Subjects: Groups & group theory; Theory Of Groups; Mathematics; Science/Mathematics; General; Mathematics / General; quantum groups; representation theory; ring theory; Group Theory
First sentence: The origins of the subject of quantum groups lie in mathematical physics, about which we will say nothing except that it is the source of the word 'quantum' in the subject.
Description: 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.