**Translations of Mathematical Monographs**

2006;
430 pp;
Hardcover

MSC: Primary 20;
Secondary 17

**Print ISBN: 978-0-8218-3731-3
Product Code: MMONO/228**

List Price: $129.00

AMS Member Price: $103.20

MAA Member Price: $116.10

**Electronic ISBN: 978-1-4704-4652-9
Product Code: MMONO/228.E**

List Price: $129.00

AMS Member Price: $103.20

MAA Member Price: $116.10

#### Supplemental Materials

# Principal Structures and Methods of Representation Theory

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*D. Zhelobenko*

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.

#### Readership

Graduate students and research mathematicians interested in representation theory.

#### Table of Contents

# Table of Contents

## Principal Structures and Methods of Representation Theory

- Cover Cover11
- Title page iii4
- Contents v6
- Preface ix10
- Introduction 114
- Basic notions 316
- General theory 4962
- Associative algebras 5164
- Lie algebras 99112
- Topological groups 139152
- Lie groups 187200
- Special topics 225238
- Semisimple Lie algebras 227240
- Semisimple Lie groups 263276
- Banach algebras 301314
- Quantum groups 347360
- Root systems 391404
- Banach spaces 403416
- Convex sets 407420
- The algebra 𝐵(𝐻) 413426
- Bibliography 421434
- Index 425438
- Back Cover Back Cover1446