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Introduction to Quantum Groups

2010-10-27 Mathematics
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Release : 2010-10-27
Genre : Mathematics
Kind : eBook
Book Rating : 171/5 ( reviews)

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Book Synopsis Introduction to Quantum Groups by : George Lusztig

Download or read book Introduction to Quantum Groups written by George Lusztig. This book was released on 2010-10-27. 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.

Introduction to Quantum Groups and Crystal Bases

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 746/5 ( reviews)

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Book Synopsis Introduction to Quantum Groups and Crystal Bases by : Jin Hong

Download or read book Introduction to Quantum Groups and Crystal Bases written by Jin Hong. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: 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

2012-12-06 Science
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Release : 2012-12-06
Genre : Science
Kind : eBook
Book Rating : 965/5 ( reviews)

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Book Synopsis Quantum Groups and Their Representations by : Anatoli Klimyk

Download or read book Quantum Groups and Their Representations written by Anatoli Klimyk. This book was released on 2012-12-06. 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.

Lectures on Quantum Groups

2010 Mathematical physics
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Release : 2010
Genre : Mathematical physics
Kind : eBook
Book Rating : 077/5 ( reviews)

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Book Synopsis Lectures on Quantum Groups by : Pavel I. Etingof

Download or read book Lectures on Quantum Groups written by Pavel I. Etingof. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt:

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

2013-11-22 Mathematics
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Release : 2013-11-22
Genre : Mathematics
Kind : eBook
Book Rating : 093/5 ( reviews)

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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. This book was released on 2013-11-22. 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.

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