Lectures On Algebraic Quantum Groups PDF Download
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| 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 | : Ken A Brown |
| Publisher | : |
| Total Pages | : 364 |
| Release | : 2002-04-01 |
| Genre | : |
| ISBN | : 9783034882064 |
Download Lectures on Algebraic Quantum Groups Book in PDF, ePub and Kindle
| Author | : Jens Carsten Jantzen |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 282 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 0821804782 |
Download Lectures on Quantum Groups Book in PDF, ePub and Kindle
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.
| Author | : Benjamin Enriquez |
| Publisher | : European Mathematical Society |
| Total Pages | : 148 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 9783037190470 |
Download Quantum Groups Book in PDF, ePub and Kindle
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 | : Pavel I. Etingof |
| Publisher | : |
| Total Pages | : 264 |
| Release | : 2002 |
| Genre | : Mathematical physics |
| ISBN | : |
Download Lectures on Quantum Groups Book in PDF, ePub and Kindle
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.
| Author | : Mo-lin Ge |
| Publisher | : World Scientific |
| Total Pages | : 242 |
| Release | : 1992-05-30 |
| Genre | : |
| ISBN | : 9814555835 |
Download Quantum Group And Quantum Integrable Systems - Nankai Lectures On Mathematical Physics Book in PDF, ePub and Kindle
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.
| Author | : L.A. Lambe |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 314 |
| Release | : 2013-11-22 |
| Genre | : Mathematics |
| ISBN | : 1461541093 |
Download Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach Book in PDF, ePub and Kindle
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.
| 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 | : Thomas Timmermann |
| Publisher | : European Mathematical Society |
| Total Pages | : 436 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 9783037190432 |
Download An Invitation to Quantum Groups and Duality Book in PDF, ePub and Kindle
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 | : Louis Boutet de Monvel |
| Publisher | : Springer |
| Total Pages | : 226 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540481958 |
Download D-modules, Representation Theory, and Quantum Groups Book in PDF, ePub and Kindle
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.
