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Differential Geometry, Lie Groups, and Symmetric Spaces
Sigurdur Helgason
Price
2095.00
ISBN
9780821852170
Language
English
Pages
668
Format
Paperback
Dimensions
180 x 240 mm
Year of Publishing
2010
Territorial Rights
Restricted
Imprint
American Mathematical Society
Catalogues

For many years and for many mathematicians, Sigurdur Helgason''s classic has been—and continues to be—the standard source for this material. Helgason begins with a concise, self-contained introduction to differential geometry. He then introduces Lie groups and Lie algebras, including important results on their structure. This sets the stage for the introduction and study of symmetric spaces, which form the central part of the book. The text concludes with the classification of symmetric spaces by means of the Killing-Cartan classification of simple Lie algebras over C and Cartan''s classification of simple Lie algebras over R. The excellent exposition is supplemented by extensive collections of useful exercises at the end of each chapter. All the problems have either solutions or substantial hints, found at the back of the book. For this latest edition, Helgason has made corrections and added helpful notes and useful references. Sigurdur Helgason was awarded the Steele Prize for Differential Geometry, Lie Groups, and Symmetric Spaces and Groups and Geometric Analysis.

Sigurdur Helgason, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA.
  • Elementary differential geometry
  • Lie groups and Lie algebras
  • Structure of semisimple Lie algebras
  • Symmetric spaces
  • Decomposition of symmetric spaces
  • Symmetric spaces of the noncompact type
  • Symmetric spaces of the compact type
  • Hermitian symmetric spaces
  • Structure of semisimple Lie groups
  • The classification of simple Lie algebras and of symmetric spaces
  • Solutions to exercises
  • Some details
  • Bibliography
    List of notational conventions
    Symbols frequently used
    Index
    Reviews for the first edition
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