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Lie Groups
Mikio Ise, Masaru Takeuchi, and Masaru Takeuchi
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Translations of Mathematical Monographs
1991; 259 pp; softcover
Volume: 85
Reprint/Revision History:
reprinted with corrections 1996, third printing 2001
ISBN-10: 0-8218-4544-6
ISBN-13: 978-0-8218-4544-8
List Price: US$94
Member Price: US$75.20
Order Code: MMONO/85
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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.

Reviews

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

-- Zentralblatt MATH

Table of Contents

Part I
  • Concept of Lie group, particularly, linear Lie group
  • Compact Lie groups and semisimple Lie groups
  • Outline of the theory of Lie algebras
Part II
  • Riemannian manifolds
  • Riemannian symmetric spaces
  • Riemannian symmetric spaces of semisimple type
  • Hermitian symmetric spaces
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