Lectures on Algebraic Quantum Groups

Ken R. Goodearl

ISBN 10: 3764367148 / ISBN 13: 9783764367145

Verlag: Birkhäuser Basel, Birkhäuser Basel Apr 2002, 2002

Beschreibung

Neuware -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).Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 364 pp. Englisch. Bestandsnummer des Verkäufers 9783764367145

Bibliografische Details

Titel: Lectures on Algebraic Quantum Groups

Verlag: Birkhäuser Basel, Birkhäuser Basel Apr 2002

Erscheinungsdatum: 2002

Einband: Taschenbuch

Zustand: Neu

Über diesen Titel

Inhaltsangabe:

This book consists of an expanded set of lectures on algebraic aspects of quantum groups. It particularly concentrates on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras. Large parts of the material are developed in full textbook style, featuring many examples and numerous exercises; other portions are discussed with sketches of proofs, while still other material is quoted without proof.

Críticas:

"The proofs, sketches of proofs, and quotations from the literature are carefully written. Numerous examples and exercises are included, and bibliographical notes conclude each chapter. The second and third parts end with a discussion of open problems and perspectives for further research."

--Mathematical Reviews