Introduction to Quantum Groups

Introduction to Quantum Groups
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.

Introduction to Quantum Groups and Crystal Bases

Introduction to Quantum Groups and Crystal Bases
Author: Jin Hong
Publisher: American Mathematical Soc.
Total Pages: 327
Release: 2002
Genre: Mathematics
ISBN: 0821828746

The purpose of this book is to provide an elementary introduction to the theory of quantum groups and crystal bases, focusing on the combinatorial aspects of the theory.

Quantum Groups and Their Representations

Quantum Groups and Their Representations
Author: Anatoli Klimyk
Publisher: Springer Science & Business Media
Total Pages: 568
Release: 2012-12-06
Genre: Science
ISBN: 3642608965

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.

Quantum Groups

Quantum Groups
Author: Christian Kassel
Publisher: Springer Science & Business Media
Total Pages: 540
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461207835

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.

A Quantum Groups Primer

A Quantum Groups Primer
Author: Shahn Majid
Publisher: Cambridge University Press
Total Pages: 183
Release: 2002-04-04
Genre: Mathematics
ISBN: 0521010411

Self-contained introduction to quantum groups as algebraic objects, suitable as a textbook for graduate courses.

Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach

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

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.

Foundations of Quantum Group Theory

Foundations of Quantum Group Theory
Author: Shahn Majid
Publisher: Cambridge University Press
Total Pages: 668
Release: 2000
Genre: Group theory
ISBN: 9780521648684

A graduate level text which systematically lays out the foundations of Quantum Groups.

Affine Lie Algebras and Quantum Groups

Affine Lie Algebras and Quantum Groups
Author: Jürgen Fuchs
Publisher: Cambridge University Press
Total Pages: 452
Release: 1995-03-09
Genre: Mathematics
ISBN: 9780521484121

This is an introduction to the theory of affine Lie Algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered in conformal field theory.