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Author : Shahn Majid
Publisher : Cambridge University Press
Page : 183 pages
File Size : 51,6 Mb
Release : 2002-04-04
Category : Mathematics
ISBN : 9780521010412
Self-contained introduction to quantum groups as algebraic objects, suitable as a textbook for graduate courses.
Author : George Lusztig
Publisher : Springer Science & Business Media
Page : 361 pages
File Size : 48,9 Mb
Release : 2010-10-27
Category : Mathematics
ISBN : 9780817647179
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 : Vyjayanthi Chari,Andrew N. Pressley
Publisher : Cambridge University Press
Page : 672 pages
File Size : 44,7 Mb
Release : 1995-07-27
Category : Mathematics
ISBN : 0521558840
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 : Benjamin Enriquez
Publisher : European Mathematical Society
Page : 148 pages
File Size : 45,5 Mb
Release : 2008
Category : Mathematics
ISBN : 3037190477
The volume starts with a lecture course by P. Etingof on tensor categories (notes by D. Calaque). This course is an introduction to tensor categories, leading to topics of recent research such as realizability of fusion rings, Ocneanu rigidity, module categories, weak Hopf algebras, Morita theory for tensor categories, lifting theory, categorical dimensions, Frobenius-Perron dimensions, and the classification of tensor categories. The remainder of the book consists of three detailed expositions on associators and the Vassiliev invariants of knots, classical and quantum integrable systems and elliptic algebras, and the groups of algebra automorphisms of quantum groups. The preface puts the results presented in perspective. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume gives an overview of the ongoing research in the domain of quantum groups, an important subject of current mathematical physics.
Author : Ken Brown,Ken R. Goodearl
Publisher : Birkhäuser
Page : 339 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882057
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 : Andrew Pressley
Publisher : Cambridge University Press
Page : 254 pages
File Size : 47,7 Mb
Release : 2001
Category : Mathematics
ISBN : 0521010403
Leading researchers discuss quantum groups and integrable systems, for graduates and researchers.
Author : Shahn Majid
Publisher : Cambridge University Press
Page : 668 pages
File Size : 46,7 Mb
Release : 2000
Category : Group theory
ISBN : 0521648688
A graduate level text which systematically lays out the foundations of Quantum Groups.
Author : Thomas Timmermann
Publisher : European Mathematical Society
Page : 436 pages
File Size : 41,8 Mb
Release : 2008
Category : Mathematics
ISBN : 3037190434
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 : L. C. Biedenharn,M. A. Lohe
Publisher : World Scientific
Page : 305 pages
File Size : 48,6 Mb
Release : 1995
Category : Science
ISBN : 9789810223311
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 : Anatoli Klimyk,Konrad Schmüdgen
Publisher : Springer Science & Business Media
Page : 568 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642608964
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 : Bangming Deng
Publisher : American Mathematical Soc.
Page : 790 pages
File Size : 55,6 Mb
Release : 2008
Category : Finite fields (Algebra).
ISBN : 9780821841860
"The interplay between finite dimensional algebras and Lie theory dates back many years. In more recent times, these interrelations have become even more strikingly apparent. This text combines, for the first time in book form, the theories of finite dimensional algebras and quantum groups. More precisely, it investigates the Ringel-Hall algebra realization for the positive part of a quantum enveloping algebra associated with a symmetrizable Cartan matrix and it looks closely at the Beilinson-Lusztig-MacPherson realization for the entire quantum $\mathfrak{gl}_n$. The book begins with the two realizations of generalized Cartan matrices, namely, the graph realization and the root datum realization. From there, it develops the representation theory of quivers with automorphisms and the theory of quantum enveloping algebras associated with Kac-Moody Lie algebras. These two independent theories eventually meet in Part 4, under the umbrella of Ringel-Hall algebras. Cartan matrices can also be used to define an important class of groups--Coxeter groups--and their associated Hecke algebras. Hecke algebras associated with symmetric groups give rise to an interesting class of quasi-hereditary algebras, the quantum Schur algebras. The structure of these finite dimensional algebras is used in Part 5 to build the entire quantum $\mathfrak{gl}_n$ through a completion process of a limit algebra (the Beilinson-Lusztig-MacPherson algebra). The book is suitable for advanced graduate students. Each chapter concludes with a series of exercises, ranging from the routine to sketches of proofs of recent results from the current literature."--Publisher's website.
Author : Florin Felix Nichita
Publisher : MDPI
Page : 239 pages
File Size : 42,6 Mb
Release : 2019-01-31
Category : Mathematics
ISBN : 9783038973249
This book is a printed edition of the Special Issue "Hopf Algebras, Quantum Groups and Yang-Baxter Equations" that was published in Axioms
Author : Ross Street
Publisher : Unknown
Page : 141 pages
File Size : 53,9 Mb
Release : 2007
Category : Algebra
ISBN : 0511269323
Quantum Groups: A Path to Current Algebra presents the latest algebraic concepts and techniques.
Author : Christian Kassel
Publisher : Springer Science & Business Media
Page : 540 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461207832
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 : Jens Carsten Jantzen
Publisher : American Mathematical Soc.
Page : 280 pages
File Size : 47,8 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 0821872346
Starting with the quantum analog of sl2, the author carefully leads the reader through all the details necessary for full understanding of the subject, particularly emphasizing similarities and differences with the classical theory. The final chapters of the book describe the Kashiwara-Lusztig theory of so-called crystal (or canonical) bases in representations of complex semisimple Lie algebra.
