Quantum Groups And Their Representations
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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 | : Anatoli Klimyk |
Publisher | : Springer |
Total Pages | : 0 |
Release | : 2011-12-14 |
Genre | : Science |
ISBN | : 9783642646010 |
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 | : Anatoli Klimyk |
Publisher | : Springer |
Total Pages | : 552 |
Release | : 2011-12-22 |
Genre | : Science |
ISBN | : 9783642608971 |
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Author | : Peter Woit |
Publisher | : Springer |
Total Pages | : 659 |
Release | : 2017-11-01 |
Genre | : Science |
ISBN | : 3319646125 |
Download Quantum Theory, Groups and Representations Book in PDF, Epub and Kindle
This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.
Author | : Ken Brown |
Publisher | : Birkhäuser |
Total Pages | : 339 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 303488205X |
Download Lectures on Algebraic Quantum Groups Book in PDF, Epub and Kindle
This book consists of an expanded set of lectures on algebraic aspects of quantum groups. It particularly concentrates on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras. Large parts of the material are developed in full textbook style, featuring many examples and numerous exercises; other portions are discussed with sketches of proofs, while still other material is quoted without proof.
Author | : Toshiaki Shoji |
Publisher | : American Mathematical Society(RI) |
Total Pages | : 514 |
Release | : 2004 |
Genre | : Computers |
ISBN | : |
Download Representation Theory of Algebraic Groups and Quantum Groups Book in PDF, Epub and Kindle
A collection of research and survey papers written by speakers at the Mathematical Society of Japan's 10th International Conference. This title presents an overview of developments in representation theory of algebraic groups and quantum groups. It includes papers containing results concerning Lusztig's conjecture on cells in affine Weyl groups.
Author | : Vyjayanthi Chari |
Publisher | : Cambridge University Press |
Total Pages | : 672 |
Release | : 1995-07-27 |
Genre | : Mathematics |
ISBN | : 9780521558846 |
Download A Guide to Quantum Groups Book in PDF, Epub and Kindle
Since they first arose in the 1970s and early 1980s, quantum groups have proved to be of great interest to mathematicians and theoretical physicists. The theory of quantum groups is now well established as a fascinating chapter of representation theory, and has thrown new light on many different topics, notably low-dimensional topology and conformal field theory. The goal of this book is to give a comprehensive view of quantum groups and their applications. The authors build on a self-contained account of the foundations of the subject and go on to treat the more advanced aspects concisely and with detailed references to the literature. Thus this book can serve both as an introduction for the newcomer, and as a guide for the more experienced reader. All who have an interest in the subject will welcome this unique treatment of quantum groups.
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 | : Jürg Fröhlich |
Publisher | : Springer |
Total Pages | : 438 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540476113 |
Download Quantum Groups, Quantum Categories and Quantum Field Theory Book in PDF, Epub and Kindle
This book reviews recent results on low-dimensional quantum field theories and their connection with quantum group theory and the theory of braided, balanced tensor categories. It presents detailed, mathematically precise introductions to these subjects and then continues with new results. Among the main results are a detailed analysis of the representation theory of U (sl ), for q a primitive root of unity, and a semi-simple quotient thereof, a classfication of braided tensor categories generated by an object of q-dimension less than two, and an application of these results to the theory of sectors in algebraic quantum field theory. This clarifies the notion of "quantized symmetries" in quantum fieldtheory. The reader is expected to be familiar with basic notions and resultsin algebra. The book is intended for research mathematicians, mathematical physicists and graduate students.
Author | : Jin Hong |
Publisher | : American Mathematical Soc. |
Total Pages | : 327 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 0821828746 |
Download Introduction to Quantum Groups and Crystal Bases Book in PDF, Epub and Kindle
The purpose of this book is to provide an elementary introduction to the theory of quantum groups and crystal bases, focusing on the combinatorial aspects of the theory.