Hardcover ISBN:  9780821837313 
Product Code:  MMONO/228 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
Electronic ISBN:  9781470446529 
Product Code:  MMONO/228.E 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 

Book DetailsTranslations of Mathematical MonographsVolume: 228; 2006; 430 ppMSC: Primary 20; Secondary 17;
The main topic of this book can be described as the theory of algebraic and topological structures admitting natural representations by operators in vector spaces. These structures include topological algebras, Lie algebras, topological groups, and Lie groups.
The book is divided into three parts. Part I surveys general facts for beginners, including linear algebra and functional analysis. Part II considers associative algebras, Lie algebras, topological groups, and Lie groups, along with some aspects of ring theory and the theory of algebraic groups. The author provides a detailed account of classical results in related branches of mathematics, such as invariant integration and Lie's theory of connections between Lie groups and Lie algebras. Part III discusses semisimple Lie algebras and Lie groups, Banach algebras, and quantum groups.
This is a useful text for a wide range of specialists, including graduate students and researchers working in mathematical physics and specialists interested in modern representation theory. It is suitable for independent study or supplementary reading.
Also available from the AMS by this acclaimed author is Compact Lie Groups and Their Representations.ReadershipGraduate students and research mathematicians interested in representation theory.

Table of Contents

Introduction

Basic notions

General theory

Associative algebras

Lie algebras

Topological groups

Lie groups

Special topics

Semisimple Lie algebras

Semisimple Lie groups

Banach algebras

Quantum groups

Root systems

Banach spaces

Convex sets

The algebra $\mathrm {B}(H)$


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The main topic of this book can be described as the theory of algebraic and topological structures admitting natural representations by operators in vector spaces. These structures include topological algebras, Lie algebras, topological groups, and Lie groups.
The book is divided into three parts. Part I surveys general facts for beginners, including linear algebra and functional analysis. Part II considers associative algebras, Lie algebras, topological groups, and Lie groups, along with some aspects of ring theory and the theory of algebraic groups. The author provides a detailed account of classical results in related branches of mathematics, such as invariant integration and Lie's theory of connections between Lie groups and Lie algebras. Part III discusses semisimple Lie algebras and Lie groups, Banach algebras, and quantum groups.
This is a useful text for a wide range of specialists, including graduate students and researchers working in mathematical physics and specialists interested in modern representation theory. It is suitable for independent study or supplementary reading.
Also available from the AMS by this acclaimed author is Compact Lie Groups and Their Representations.
Graduate students and research mathematicians interested in representation theory.

Introduction

Basic notions

General theory

Associative algebras

Lie algebras

Topological groups

Lie groups

Special topics

Semisimple Lie algebras

Semisimple Lie groups

Banach algebras

Quantum groups

Root systems

Banach spaces

Convex sets

The algebra $\mathrm {B}(H)$