Lectures on Quantum Groups
| Author | : Pavel I. Etingof |
| Publisher | : |
| Total Pages | : 242 |
| Release | : 2010 |
| Genre | : Mathematical physics |
| ISBN | : 9781571462077 |
Download Lectures on Quantum Groups Book in PDF, ePub and Kindle
Lectures On Quantum Groups PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Lectures On Quantum Groups PDF full book. Access full book title Lectures On Quantum Groups.
Lectures on Algebraic Quantum Groups
| 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.
Lectures on Quantum Groups
| 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.
Lectures on Quantum Mechanics for Mathematics Students
| Author | : L. D. Faddeev |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 250 |
| Release | : 2009 |
| Genre | : Quantum theory |
| ISBN | : 082184699X |
Download Lectures on Quantum Mechanics for Mathematics Students Book in PDF, ePub and Kindle
Describes the relation between classical and quantum mechanics. This book contains a discussion of problems related to group representation theory and to scattering theory. It intends to give a mathematically oriented student the opportunity to grasp the main points of quantum theory in a mathematical framework.
Quantum Groups and Noncommutative Geometry
| Author | : Yuri I. Manin |
| Publisher | : Springer |
| Total Pages | : 125 |
| Release | : 2018-10-11 |
| Genre | : Mathematics |
| ISBN | : 3319979876 |
Download Quantum Groups and Noncommutative Geometry Book in PDF, ePub and Kindle
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.
Introduction to Quantum Groups
| Author | : George Lusztig |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 361 |
| Release | : 2010-10-27 |
| Genre | : Mathematics |
| ISBN | : 0817647171 |
Download Introduction to Quantum Groups Book in PDF, ePub and Kindle
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.
Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach
| 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.
Quantum Groups
| Author | : Christian Kassel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 540 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461207835 |
Download Quantum Groups Book in PDF, ePub and Kindle
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.
Lectures on Quantum Mechanics
| Author | : Philip L. Bowers |
| Publisher | : Cambridge University Press |
| Total Pages | : 585 |
| Release | : 2020-09-17 |
| Genre | : Science |
| ISBN | : 1108429769 |
Download Lectures on Quantum Mechanics Book in PDF, ePub and Kindle
A leisurely but mathematically honest presentation of quantum mechanics for graduate students in mathematics with an interest in physics.
Tensor Categories
| Author | : Pavel Etingof |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 344 |
| Release | : 2016-08-05 |
| Genre | : Algebraic topology |
| ISBN | : 1470434415 |
Download Tensor Categories Book in PDF, ePub and Kindle
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.
