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Algebras of Functions on Quantum Groups: Part I

1998 Mathematics
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Release : 1998
Genre : Mathematics
Kind : eBook
Book Rating : 360/5 ( reviews)

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Book Synopsis Algebras of Functions on Quantum Groups: Part I by : Leonid I. Korogodski

Download or read book Algebras of Functions on Quantum Groups: Part I written by Leonid I. Korogodski. This book was released on 1998. Available in PDF, EPUB and Kindle. Book excerpt: The text is devoted to the study of algebras of functions on quantum groups. The book includes the theory of Poisson-Lie algebras (quasi-classical version of algebras of functions on quantum groups), a description of representations of algebras of functions and the theory of quantum Weyl groups. It can serve as a text for an introduction to the theory of quantum groups and is intended for graduate students and research mathematicians working in algebra, representation theory and mathematical physics.

Quantum Groups and Their Representations

2012-12-06 Science
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Release : 2012-12-06
Genre : Science
Kind : eBook
Book Rating : 965/5 ( reviews)

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Book Synopsis Quantum Groups and Their Representations by : Anatoli Klimyk

Download or read book Quantum Groups and Their Representations written by Anatoli Klimyk. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Quantum Groups

1996 Science
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Release : 1996
Genre : Science
Kind : eBook
Book Rating : 237/5 ( reviews)

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Book Synopsis Introduction to Quantum Groups by : Masud Chaichian

Download or read book Introduction to Quantum Groups written by Masud Chaichian. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt: In the past decade there has been an extemely rapid growth in the interest and development of quantum group theory.This book provides students and researchers with a practical introduction to the principal ideas of quantum groups theory and its applications to quantum mechanical and modern field theory problems. It begins with a review of, and introduction to, the mathematical aspects of quantum deformation of classical groups, Lie algebras and related objects (algebras of functions on spaces, differential and integral calculi). In the subsequent chapters the richness of mathematical structure and power of the quantum deformation methods and non-commutative geometry is illustrated on the different examples starting from the simplest quantum mechanical system — harmonic oscillator and ending with actual problems of modern field theory, such as the attempts to construct lattice-like regularization consistent with space-time Poincaré symmetry and to incorporate Higgs fields in the general geometrical frame of gauge theories. Graduate students and researchers studying the problems of quantum field theory, particle physics and mathematical aspects of quantum symmetries will find the book of interest.

Algebras of Functions on Quantum Groups

1998 Function algebras
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Author :
Release : 1998
Genre : Function algebras
Kind : eBook
Book Rating : 363/5 ( reviews)

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Book Synopsis Algebras of Functions on Quantum Groups by : Leonid I. Korogodski

Download or read book Algebras of Functions on Quantum Groups written by Leonid I. Korogodski. This book was released on 1998. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Quantum Groups

2010-10-27 Mathematics
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Release : 2010-10-27
Genre : Mathematics
Kind : eBook
Book Rating : 171/5 ( reviews)

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Book Synopsis Introduction to Quantum Groups by : George Lusztig

Download or read book Introduction to Quantum Groups written by George Lusztig. This book was released on 2010-10-27. Available in PDF, EPUB and Kindle. Book excerpt: The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties. This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the book could also be used as a text book.

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