An Introduction to Lie Groups and the Geometry of Homogeneous Spaces

Andreas Arvanitoyeorgos

ISBN 10: 0821827782 / ISBN 13: 9780821827789

Published by American Mathematical Society, 2003

About this Item

2003. Paperback. The theory of Lie groups involves many areas of mathematics: algebra, differential geometry, algebraic geometry, analysis, and differential equations. This work outlines the prerequisites to get the reader started, and then chooses a path through this theory that aims for an understanding of the geometry of Lie groups and homogeneous spaces. Series: Student Mathematical Library. Num Pages: 141 pages. BIC Classification: PBF. Category: (P) Professional & Vocational. Dimension: 215 x 141 x 10. Weight in Grams: 192. . . . . . Books ship from the US and Ireland.

Seller Inventory # V9780821827789

Bibliographic Details

• Title: An Introduction to Lie Groups and the Geometry of Homogeneous Spaces
• Publisher: American Mathematical Society
• Publication Date: 2003
• Language: English
• ISBN 10: 0821827782
• ISBN 13: 9780821827789
• Binding: Soft cover
• Condition: New

About this title

Synopsis

It is remarkable that so much about Lie groups could be packed into this small book. But after reading it, students will be well-prepared to continue with more advanced, graduate-level topics in differential geometry or the theory of Lie groups. <P>The theory of Lie groups involves many areas of mathematics: algebra, differential geometry, algebraic geometry, analysis, and differential equations. In this book, Arvanitoyeorgos outlines enough of the prerequisites to get the reader started. He then chooses a path through this rich and diverse theory that aims for an understanding of the geometry of Lie groups and homogeneous spaces. In this way, he avoids the extra detail needed for a thorough discussion of representation theory. <P>Lie groups and homogeneous spaces are especially useful to study in geometry, as they provide excellent examples where quantities (such as curvature) are easier to compute. A good understanding of them provides lasting intuition, especially in differential geometry. <P>The author provides several examples and computations. Topics discussed include the classification of compact and connected Lie groups, Lie algebras, geometrical aspects of compact Lie groups and reductive homogeneous spaces, and important classes of homogeneous spaces, such as symmetric spaces and flag manifolds. Applications to more advanced topics are also included, such as homogeneous Einstein metrics, Hamiltonian systems, and homogeneous geodesics in homogeneous spaces.