Anatoli Klimyk, Konrad Schmüdgen

Quantum Groups and Their Representations (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 552
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783642608964
• Artikelnr.: 53149903

Inhaltsangabe

I. An Introduction to Quantum Groups.- 1. Hopf Algebras.- 2. q-Calculus.- 3. The Quantum Algebra Uq(sl2) and Its Representations.- 4. The Quantum Group SLq(2) and Its Representations.- 5. The q-Oscillator Algebras and Their Representations.- II. Quantized Universal Enveloping Algebras.- 6. Drinfeld-Jimbo Algebras.- 7. Finite-Dimensional Representations of Drinfeld-Jimbo Algebras.- 8. Quasitriangularity and Universal R-Matrices.- III. Quantized Algebras of Functions.- 9. Coordinate Algebras of Quantum Groups and Quantum Vector Spaces.- 10. Coquasitriangularity and Crossed Product Constructions.- 11. Corepresentation Theory and Compact Quantum Groups.- IV. Noncommutative Differential Calculus.- 12. Covariant Differential Calculus on Quantum Spaces.- 13. Hopf Bimodules and Exterior Algebras.- 14. Covariant Differential Calculus on Quantum Groups.

Rezensionen

From the reviews
"Klimyk and Schmüdgen are kind to their readers. Proofs are given in full, and there are helpful explanations of the basic concepts ... the book has the virtue of comprehensivness in its chose range of topics. It is easy to dip into and use as a reference book." (A. Sudbery, Bulletin of the London Mathematical Society, 2000)