Ebook: Quantum Groups and Their Representations

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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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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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.
Content:
Front Matter....Pages I-XIX
Front Matter....Pages 1-1
Hopf Algebras....Pages 3-36
q-Calculus....Pages 37-52
The Quantum Algebra U q (sl2)and Its Representations....Pages 53-96
The Quantum Group SL q (2) and Its Representations....Pages 97-132
The q-Oscillator Algebras and Their Representations....Pages 133-154
Front Matter....Pages 155-155
Drinfeld-Jimbo Algebras....Pages 157-196
Finite-Dimensional Representations of Drinfeld-Jimbo Algebras....Pages 197-242
Quasitriangularity and Universal R-Matrices....Pages 243-300
Front Matter....Pages 301-301
Coordinate Algebras of Quantum Groups and Quantum Vector Spaces....Pages 303-330
Coquasitriangularity and Crossed Product Constructions....Pages 331-394
Corepresentation Theory and Compact Quantum Groups....Pages 395-454
Front Matter....Pages 455-455
Covariant Differential Calculus on Quantum Spaces....Pages 457-472
Hopf Bimodules and Exterior Algebras....Pages 473-490
Covariant Differential Calculus on Quantum Groups....Pages 491-528
Back Matter....Pages 529-552

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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.
Content:
Front Matter....Pages I-XIX
Front Matter....Pages 1-1
Hopf Algebras....Pages 3-36
q-Calculus....Pages 37-52
The Quantum Algebra U q (sl2)and Its Representations....Pages 53-96
The Quantum Group SL q (2) and Its Representations....Pages 97-132
The q-Oscillator Algebras and Their Representations....Pages 133-154
Front Matter....Pages 155-155
Drinfeld-Jimbo Algebras....Pages 157-196
Finite-Dimensional Representations of Drinfeld-Jimbo Algebras....Pages 197-242
Quasitriangularity and Universal R-Matrices....Pages 243-300
Front Matter....Pages 301-301
Coordinate Algebras of Quantum Groups and Quantum Vector Spaces....Pages 303-330
Coquasitriangularity and Crossed Product Constructions....Pages 331-394
Corepresentation Theory and Compact Quantum Groups....Pages 395-454
Front Matter....Pages 455-455
Covariant Differential Calculus on Quantum Spaces....Pages 457-472
Hopf Bimodules and Exterior Algebras....Pages 473-490
Covariant Differential Calculus on Quantum Groups....Pages 491-528
Back Matter....Pages 529-552
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