Quantum Groups and Their Representations
By: by Anatoli Klimyk, Konrad Schmüdgen
Contributors: Schmudgen, Konrad
Series: Texts and Monographs in Physics, 1864-5879; Texts and monographs in physics
Publisher: Springer Berlin Heidelberg
Published: 1997
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 552
ISBN-13: 9783642608964
Description: This book start with an introduction to quantum groups for the beginner and continues as a textbook for graduate students in physics and in mathematics. It can also be used as a reference by more advanced readers. The authors cover a large but well-chosen variety of subjects from the theory of quantum groups (quantized universal enveloping algebras, quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The book is written with potential applications in physics and mathematics in mind. The basic quantum groups and quantum algebras and their representations are given in detail and accompanied by explicit formulas. A number of topics and results from the more advanced general theory are developed and discussed.
Table of contents: title: I. An Introduction to Quantum Groups: Hopf Algebras.-q-Calculus; title: The Quantum Algebra Uq(sl2) and Its Representations; title: The Quantum Grouö SLq(2) and Its Representations; title: The q-Oscillator Algebras and Their Representations. II. Quantized Universal Enveloping Algebras: Drinfeld; title: Jimbo Algebras; title: Finite-Dimentional Representations of Dinfeld; title: Jimbo Algebras; title: Quasitriangularity and Universal R-Mattrices. III. Quantized Algebras of Functions; title: Coordinate Algebras of Quantum Groups and Quantum Vector Spaces; title: Coquasitriangularity and Crossed Product Constructions; title: etc.