Algebras Of Functions On Quantum Groups Part I PDF Download
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Author | : Leonid I. Korogodski |
Publisher | : American Mathematical Soc. |
Total Pages | : 162 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : 0821803360 |
Download Algebras of Functions on Quantum Groups: Part I Book in PDF, ePub and Kindle
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.
Author | : Leonid I. Korogodski |
Publisher | : |
Total Pages | : 149 |
Release | : 1998 |
Genre | : Function algebras |
ISBN | : 9780821803363 |
Download Algebras of Functions on Quantum Groups Book in PDF, ePub and Kindle
Author | : Anatoli Klimyk |
Publisher | : Springer Science & Business Media |
Total Pages | : 568 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 3642608965 |
Download Quantum Groups and Their Representations Book in PDF, ePub and Kindle
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.
Author | : George Lusztig |
Publisher | : Springer Science & Business Media |
Total Pages | : 361 |
Release | : 2010-10-27 |
Genre | : Mathematics |
ISBN | : 0817647171 |
Download Introduction to Quantum Groups Book in PDF, ePub and Kindle
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.
Author | : Masud Chaichian |
Publisher | : World Scientific |
Total Pages | : 357 |
Release | : 1996-11-22 |
Genre | : Science |
ISBN | : 9814499137 |
Download Introduction To Quantum Groups Book in PDF, ePub and Kindle
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.
Author | : Thomas Timmermann |
Publisher | : European Mathematical Society |
Total Pages | : 436 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 9783037190432 |
Download An Invitation to Quantum Groups and Duality Book in PDF, ePub and Kindle
This book provides an introduction to the theory of quantum groups with emphasis on their duality and on the setting of operator algebras. Part I of the text presents the basic theory of Hopf algebras, Van Daele's duality theory of algebraic quantum groups, and Woronowicz's compact quantum groups, staying in a purely algebraic setting. Part II focuses on quantum groups in the setting of operator algebras. Woronowicz's compact quantum groups are treated in the setting of $C^*$-algebras, and the fundamental multiplicative unitaries of Baaj and Skandalis are studied in detail. An outline of Kustermans' and Vaes' comprehensive theory of locally compact quantum groups completes this part. Part III leads to selected topics, such as coactions, Baaj-Skandalis-duality, and approaches to quantum groupoids in the setting of operator algebras. The book is addressed to graduate students and non-experts from other fields. Only basic knowledge of (multi-) linear algebra is required for the first part, while the second and third part assume some familiarity with Hilbert spaces, $C^*$-algebras, and von Neumann algebras.
Author | : Masud Chaichian |
Publisher | : World Scientific |
Total Pages | : 362 |
Release | : 1996 |
Genre | : Science |
ISBN | : 9789810226237 |
Download Introduction to Quantum Groups Book in PDF, ePub and Kindle
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.
Author | : Michiel Hazewinkel |
Publisher | : American Mathematical Soc. |
Total Pages | : 425 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 0821852620 |
Download Algebras, Rings and Modules Book in PDF, ePub and Kindle
Presenting an introduction to the theory of Hopf algebras, the authors also discuss some important aspects of the theory of Lie algebras. This book includes a chapters on the Hopf algebra of symmetric functions, the Hopf algebra of representations of the symmetric groups, the Hopf algebras of the nonsymmetric and quasisymmetric functions, and the Hopf algebra of permutations.
Author | : Christian Voigt |
Publisher | : Springer Nature |
Total Pages | : 382 |
Release | : 2020-09-24 |
Genre | : Mathematics |
ISBN | : 3030524639 |
Download Complex Semisimple Quantum Groups and Representation Theory Book in PDF, ePub and Kindle
This book provides a thorough introduction to the theory of complex semisimple quantum groups, that is, Drinfeld doubles of q-deformations of compact semisimple Lie groups. The presentation is comprehensive, beginning with background information on Hopf algebras, and ending with the classification of admissible representations of the q-deformation of a complex semisimple Lie group. The main components are: - a thorough introduction to quantized universal enveloping algebras over general base fields and generic deformation parameters, including finite dimensional representation theory, the Poincaré-Birkhoff-Witt Theorem, the locally finite part, and the Harish-Chandra homomorphism, - the analytic theory of quantized complex semisimple Lie groups in terms of quantized algebras of functions and their duals, - algebraic representation theory in terms of category O, and - analytic representation theory of quantized complex semisimple groups. Given its scope, the book will be a valuable resource for both graduate students and researchers in the area of quantum groups.
Author | : Leonid Lʹvovych Vaksman |
Publisher | : American Mathematical Soc. |
Total Pages | : 272 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 0821849093 |
Download Quantum Bounded Symmetric Domains Book in PDF, ePub and Kindle
Explores the basic theory of quantum bounded symmetric domains. The area became active in the late 1990s at a junction of noncommutative complex analysis and extensively developing theory of quantum groups. In a surprising advance of the theory of quantum bounded symmetric domains, it turned out that many classical problems admit elegant quantum analogs. Some of those are expounded in the book.