[PDF] Representations Of Quantum Groups In The Root Of Unity Case eBook

Author : Anatoli Klimyk
Publisher : Springer Science & Business Media
Page : 568 pages
File Size : 12,86 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 : Ansgar Wolfgang Schnizer
Publisher :
Page : 19 pages
File Size : 38,55 MB
Release : 1993
Category : Quantum groups
ISBN :

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Abstract: "Representations of Quantum Groups U[subscript [epsilon]](g[subscript n]), g[subscript n] any semi simple Lie algebra of rank n, are constructed from arbitrary representations of rank n - 1 quantum groups for [epsilon] a root of unity. Representations which have the maximal dimension and number of free parameters for irreducible representations arise as special cases."

Author : Vyjayanthi Chari
Publisher : Cambridge University Press
Page : 672 pages
File Size : 30,45 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 : Lawrence C Biedenharn
Publisher : World Scientific
Page : 305 pages
File Size : 26,74 MB
Release : 1995-08-31
Category : Science
ISBN : 9814500135

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Quantum groups are a generalization of the classical Lie groups and Lie algebras and provide a natural extension of the concept of symmetry fundamental to physics. This monograph is a survey of the major developments in quantum groups, using an original approach based on the fundamental concept of a tensor operator. Using this concept, properties of both the algebra and co-algebra are developed from a single uniform point of view, which is especially helpful for understanding the noncommuting co-ordinates of the quantum plane, which we interpret as elementary tensor operators. Representations of the q-deformed angular momentum group are discussed, including the case where q is a root of unity, and general results are obtained for all unitary quantum groups using the method of algebraic induction. Tensor operators are defined and discussed with examples, and a systematic treatment of the important (3j) series of operators is developed in detail. This book is a good reference for graduate students in physics and mathematics.

Author : Akihiko Gyoja
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 14,83 MB
Release : 2010-11-25
Category : Mathematics
ISBN : 0817646973

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Invited articles by top notch experts Focus is on topics in representation theory of algebraic groups and quantum groups Of interest to graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics