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Principal Structures and Methods of Representation Theory
 
D. Zhelobenko Moscow, Russia
Principal Structures and Methods of Representation Theory
Hardcover ISBN:  978-0-8218-3731-3
Product Code:  MMONO/228
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4652-9
Product Code:  MMONO/228.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-3731-3
eBook: ISBN:  978-1-4704-4652-9
Product Code:  MMONO/228.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
Principal Structures and Methods of Representation Theory
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Principal Structures and Methods of Representation Theory
D. Zhelobenko Moscow, Russia
Hardcover ISBN:  978-0-8218-3731-3
Product Code:  MMONO/228
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4652-9
Product Code:  MMONO/228.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-3731-3
eBook ISBN:  978-1-4704-4652-9
Product Code:  MMONO/228.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 2282006; 430 pp
    MSC: 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.

    Readership

    Graduate 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 $\mathrm {B}(H)$
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2282006; 430 pp
MSC: 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.

Readership

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 $\mathrm {B}(H)$
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.