[PDF] Quantum Groups eBook

Author : Christian Kassel
Publisher : Springer Science & Business Media
Page : 540 pages
File Size : 50,10 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461207835

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Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions. It presents the quantum groups attached to SL2 as well as the basic concepts of the theory of Hopf algebras. Coverage also focuses on Hopf algebras that produce solutions of the Yang-Baxter equation and provides an account of Drinfeld's elegant treatment of the monodromy of the Knizhnik-Zamolodchikov equations.

Author : Anatoli Klimyk
Publisher : Springer Science & Business Media
Page : 568 pages
File Size : 28,38 MB
Release : 2012-12-06
Category : Science
ISBN : 3642608965

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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.

Author : George Lusztig
Publisher : Springer Science & Business Media
Page : 361 pages
File Size : 35,76 MB
Release : 2010-10-27
Category : Mathematics
ISBN : 0817647171

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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 : Ken Brown
Publisher : Birkhäuser
Page : 339 pages
File Size : 45,50 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 303488205X

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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 : Vyjayanthi Chari
Publisher : Cambridge University Press
Page : 672 pages
File Size : 44,91 MB
Release : 1995-07-27
Category : Mathematics
ISBN : 9780521558846

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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 : Jin Hong
Publisher : American Mathematical Soc.
Page : 327 pages
File Size : 13,41 MB
Release : 2002
Category : Mathematics
ISBN : 0821828746

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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.

Author : Shahn Majid
Publisher : Cambridge University Press
Page : 668 pages
File Size : 37,99 MB
Release : 2000
Category : Group theory
ISBN : 9780521648684

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A graduate level text which systematically lays out the foundations of Quantum Groups.

Author : Jürg Fröhlich
Publisher : Springer
Page : 438 pages
File Size : 38,21 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540476113

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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 : Shahn Majid
Publisher : Cambridge University Press
Page : 183 pages
File Size : 38,27 MB
Release : 2002-04-04
Category : Mathematics
ISBN : 0521010411

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Self-contained introduction to quantum groups as algebraic objects, suitable as a textbook for graduate courses.