**Translations of Mathematical Monographs**

1991;
259 pp;
Softcover

MSC: Primary 22;
Secondary 17

**Print ISBN: 978-0-8218-4544-8
Product Code: MMONO/85**

List Price: $99.00

AMS Member Price: $79.20

MAA Member Price: $89.10

**Electronic ISBN: 978-1-4704-4793-9
Product Code: MMONO/85.E**

List Price: $99.00

AMS Member Price: $79.20

MAA Member Price: $89.10

# Lie Groups

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*Masaru Takeuchi*

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.

#### Reviews & Endorsements

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

-- Zentralblatt MATH

#### Table of Contents

# Table of Contents

## Lie Groups

- Cover Cover11
- Title page i2
- Contents iii4
- Lie Groups I 16
- Contents of Lie Groups I 38
- Preface to Lie Groups I 510
- Foreword to Lie Groups I 712
- Foreword to the First Edition of Lie Groups I 914
- Notation to Lie Groups I 1116
- Chapter I. Concept of Lie group, particularly, linear Lie group 1318
- Chapter II. Compact Lie groups and semisimple Lie groups 4550
- Chapter III. Outline of the theory of Lie algebras 6974
- References 111116
- Lie Groups II 113118
- Contents of Lie Groups II 115120
- Preface to Lie Groups II 117122
- Foreword to Lie Groups II 119124
- Chapter I. Riemannian manifolds 121126
- Chapter II. Riemannian symmetric spaces 165170
- Chapter III. Riemannian symmetric spaces of semisimple type 201206
- Chapter I. Hermitian symmetric spaces 227232
- References 259264
- Back Cover Back Cover1266