Lectures on Quantum Groups
Title | Lectures on Quantum Groups PDF eBook |
Author | Pavel I. Etingof |
Publisher | |
Total Pages | 242 |
Release | 2010 |
Genre | Mathematical physics |
ISBN | 9781571462077 |
Lectures on Algebraic Quantum Groups
Title | Lectures on Algebraic Quantum Groups PDF eBook |
Author | Ken Brown |
Publisher | Birkhäuser |
Total Pages | 339 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 303488205X |
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
Title | Lectures on Quantum Groups PDF eBook |
Author | Jens Carsten Jantzen |
Publisher | American Mathematical Soc. |
Total Pages | 282 |
Release | 1996 |
Genre | Mathematics |
ISBN | 0821804782 |
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
Title | Lectures on Quantum Mechanics for Mathematics Students PDF eBook |
Author | L. D. Faddeev |
Publisher | American Mathematical Soc. |
Total Pages | 250 |
Release | 2009 |
Genre | Science |
ISBN | 082184699X |
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
Title | Quantum Groups and Noncommutative Geometry PDF eBook |
Author | Yuri I. Manin |
Publisher | Springer |
Total Pages | 125 |
Release | 2018-10-11 |
Genre | Mathematics |
ISBN | 3319979876 |
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
Title | Introduction to Quantum Groups PDF eBook |
Author | George Lusztig |
Publisher | Springer Science & Business Media |
Total Pages | 361 |
Release | 2010-10-27 |
Genre | Mathematics |
ISBN | 0817647171 |
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.
Lectures on Quantum Groups
Title | Lectures on Quantum Groups PDF eBook |
Author | Pavel I. Etingof |
Publisher | |
Total Pages | 264 |
Release | 2002 |
Genre | Mathematical physics |
ISBN |
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.