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Lectures On Algebraic Quantum Groups
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Book Synopsis Lectures on Algebraic Quantum Groups by : Ken Brown
Download or read book Lectures on Algebraic Quantum Groups written by Ken Brown and published by Birkhäuser. This book was released on 2012-12-06 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures on Algebraic Quantum Groups by : Ken A Brown
Download or read book Lectures on Algebraic Quantum Groups written by Ken A Brown and published by . This book was released on 2002-04-01 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quantum Groups, Quantum Categories and Quantum Field Theory by : Jürg Fröhlich
Download or read book Quantum Groups, Quantum Categories and Quantum Field Theory written by Jürg Fröhlich and published by Springer. This book was released on 2006-11-15 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures on Quantum Groups by : Jens Carsten Jantzen
Download or read book Lectures on Quantum Groups written by Jens Carsten Jantzen and published by American Mathematical Soc.. This book was released on 1996 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material is very well motivated ... Of the various monographs available on quantum groups, this one ... seems the most suitable for most mathematicians new to the subject ... will also be appreciated by a lot of those with considerably more experience. --Bulletin of the London Mathematical Society Since its origin, the theory of quantum groups has become one of the most fascinating topics of modern mathematics, with numerous applications to several sometimes rather disparate areas, including low-dimensional topology and mathematical physics. This book is one of the first expositions that is specifically directed to students who have no previous knowledge of the subject. The only prerequisite, in addition to standard linear algebra, is some acquaintance with the classical theory of complex semisimple Lie algebras. Starting with the quantum analog of $\mathfrak{sl}_2$, 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 algebras. The choice of the topics and the style of exposition make Jantzen's book an excellent textbook for a one-semester course on quantum groups.
Book Synopsis Quantum Groups by : Benjamin Enriquez
Download or read book Quantum Groups written by Benjamin Enriquez and published by European Mathematical Society. This book was released on 2008 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach by : L.A. Lambe
Download or read book Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach written by L.A. Lambe and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chapter 1 The algebraic prerequisites for the book are covered here and in the appendix. This chapter should be used as reference material and should be consulted as needed. A systematic treatment of algebras, coalgebras, bialgebras, Hopf algebras, and represen tations of these objects to the extent needed for the book is given. The material here not specifically cited can be found for the most part in [Sweedler, 1969] in one form or another, with a few exceptions. A great deal of emphasis is placed on the coalgebra which is the dual of n x n matrices over a field. This is the most basic example of a coalgebra for our purposes and is at the heart of most algebraic constructions described in this book. We have found pointed bialgebras useful in connection with solving the quantum Yang-Baxter equation. For this reason we develop their theory in some detail. The class of examples described in Chapter 6 in connection with the quantum double consists of pointed Hopf algebras. We note the quantized enveloping algebras described Hopf algebras. Thus for many reasons pointed bialgebras are elsewhere are pointed of fundamental interest in the study of the quantum Yang-Baxter equation and objects quantum groups.
Book Synopsis Lectures on Quantum Groups by : Pavel I. Etingof
Download or read book Lectures on Quantum Groups written by Pavel I. Etingof and published by . This book was released on 2002 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on lectures given at Harvard University in 1997, this book is an introduction to the theory of quantum groups and its development between 1982 and 1997. Topics covered include: relevant quasiclassical objects; bialgebras; Hopf algebras; and lie associators.
Book Synopsis Quantum Groups by : Christian Kassel
Download or read book Quantum Groups written by Christian Kassel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Groups and Noncommutative Geometry by : Yuri I. Manin
Download or read book Quantum Groups and Noncommutative Geometry written by Yuri I. Manin and published by Springer. This book was released on 2018-10-11 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents the second edition of Manin's celebrated 1988 Montreal lectures, which influenced a new generation of researchers in algebra to take up the study of Hopf algebras and quantum groups. In this expanded write-up of those lectures, Manin systematically develops an approach to quantum groups as symmetry objects in noncommutative geometry in contrast to the more deformation-oriented approach due to Faddeev, Drinfeld, and others. This new edition contains an extra chapter by Theo Raedschelders and Michel Van den Bergh, surveying recent work that focuses on the representation theory of a number of bi- and Hopf algebras that were first introduced in Manin's lectures, and have since gained a lot of attention. Emphasis is placed on the Tannaka–Krein formalism, which further strengthens Manin's approach to symmetry and moduli-objects in noncommutative geometry.
Book Synopsis Quantum Group And Quantum Integrable Systems - Nankai Lectures On Mathematical Physics by : Mo-lin Ge
Download or read book Quantum Group And Quantum Integrable Systems - Nankai Lectures On Mathematical Physics written by Mo-lin Ge and published by World Scientific. This book was released on 1992-05-30 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the lectures given by the three speakers, M Jimbo, P P Kulish and E K Sklyanin, who are outstanding experts in their field. It is essential reading to those working in the fields of Quantum Groups, and Integrable Systems.
Book Synopsis D-modules, Representation Theory, and Quantum Groups by : Louis Boutet de Monvel
Download or read book D-modules, Representation Theory, and Quantum Groups written by Louis Boutet de Monvel and published by Springer. This book was released on 2006-11-15 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: CONTENTS: L. Boutet de Monvel: Indice de systemes differentiels.- C. De Concini, C. Procesi: Quantum groups.- P. Schapira, J.P. Schneiders: Index theorems for R-constructible sheaves and for D-modules.- N. Berline, M. Vergne: The equivariant Chern character and index of G-invariant operators.
Book Synopsis An Invitation to Quantum Groups and Duality by : Thomas Timmermann
Download or read book An Invitation to Quantum Groups and Duality written by Thomas Timmermann and published by European Mathematical Society. This book was released on 2008 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Groups and Their Representations by : Anatoli Klimyk
Download or read book Quantum Groups and Their Representations written by Anatoli Klimyk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Tensor Categories by : Pavel Etingof
Download or read book Tensor Categories written by Pavel Etingof and published by American Mathematical Soc.. This book was released on 2016-08-05 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
Book Synopsis Algebras of Functions on Quantum Groups: Part I by : Leonid I. Korogodski
Download or read book Algebras of Functions on Quantum Groups: Part I written by Leonid I. Korogodski and published by American Mathematical Soc.. This book was released on 1998 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Integrable Systems and Quantum Groups by : Ron Donagi
Download or read book Integrable Systems and Quantum Groups written by Ron Donagi and published by Springer. This book was released on 2006-11-14 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this CIME Session was to review the state of the art in the recent development of the theory of integrable systems and their relations with quantum groups. The purpose was to gather geometers and mathematical physicists to allow a broader and more complete view of these attractive and rapidly developing fields. The papers contained in this volume have at the same time the character of survey articles and of research papers, since they contain both a survey of current problems and a number of original contributions to the subject.
Book Synopsis Introduction to Quantum Groups by : George Lusztig
Download or read book Introduction to Quantum Groups written by George Lusztig and published by Springer Science & Business Media. This book was released on 2010-10-27 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
