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Softcover ISBN:  9780821845448 
Product Code:  MMONO/85 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470447939 
Product Code:  MMONO/85.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Softcover ISBN:  9780821845448 
eBook ISBN:  9781470447939 
Product Code:  MMONO/85.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 

Book DetailsTranslations of Mathematical MonographsVolume: 85; 1991; 259 ppMSC: Primary 22; Secondary 17
The first part of this book, which is the second edition of the book of the same title, is intended to provide readers with a brief introduction to the theory of Lie groups as an aid to further study by presenting the fundamental features of Lie groups as a starting point for understanding Lie algebras and Lie theory in general. In the revisions for the second edition, proofs of some of the results were added.
The second part of the book builds on some of the background developed in the first part, offering an introduction to the theory of symmetric spaces, a remarkable example of applications of Lie group theory to differential geometry. The book emphasizes this aspect by surveying the fundamentals of Riemannian manifolds and by giving detailed explanations of the way in which geometry and Lie group theory come together.

Table of Contents

Chapters

Lie Groups I

Contents of Lie Groups I

Preface to Lie Groups I

Foreword to Lie Groups I

Foreword to the First Edition of Lie Groups I

Notation to Lie Groups I

Chapter I. Concept of Lie group, particularly, linear Lie group

Chapter II. Compact Lie groups and semisimple Lie groups

Chapter III. Outline of the theory of Lie algebras

References

Lie Groups II

Contents of Lie Groups II

Preface to Lie Groups II

Foreword to Lie Groups II

Chapter I. Riemannian manifolds

Chapter II. Riemannian symmetric spaces

Chapter III. Riemannian symmetric spaces of semisimple type

Chapter I. Hermitian symmetric spaces

References


Reviews

The qualities of the book are clear exposition, elegant style of writing, careful selection of material.
Zentralblatt MATH


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The first part of this book, which is the second edition of the book of the same title, is intended to provide readers with a brief introduction to the theory of Lie groups as an aid to further study by presenting the fundamental features of Lie groups as a starting point for understanding Lie algebras and Lie theory in general. In the revisions for the second edition, proofs of some of the results were added.
The second part of the book builds on some of the background developed in the first part, offering an introduction to the theory of symmetric spaces, a remarkable example of applications of Lie group theory to differential geometry. The book emphasizes this aspect by surveying the fundamentals of Riemannian manifolds and by giving detailed explanations of the way in which geometry and Lie group theory come together.

Chapters

Lie Groups I

Contents of Lie Groups I

Preface to Lie Groups I

Foreword to Lie Groups I

Foreword to the First Edition of Lie Groups I

Notation to Lie Groups I

Chapter I. Concept of Lie group, particularly, linear Lie group

Chapter II. Compact Lie groups and semisimple Lie groups

Chapter III. Outline of the theory of Lie algebras

References

Lie Groups II

Contents of Lie Groups II

Preface to Lie Groups II

Foreword to Lie Groups II

Chapter I. Riemannian manifolds

Chapter II. Riemannian symmetric spaces

Chapter III. Riemannian symmetric spaces of semisimple type

Chapter I. Hermitian symmetric spaces

References

The qualities of the book are clear exposition, elegant style of writing, careful selection of material.
Zentralblatt MATH