**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

Individual Member Price: $103.20

#### 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.