An Introduction to Lie Groups and the Geometry of Homogeneous Spaces
About this Title
Andreas Arvanitoyeorgos, The American College of Greece, Deree Campus, Athens, Greece
Publication: The Student Mathematical Library
Publication Year 2003: Volume 22
ISBNs: 978-0-8218-2778-9 (print); 978-1-4704-2136-6 (online)
MathSciNet review: MR2011126
MSC: Primary 53C30; Secondary 22E15
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.
The theory of Lie groups involves many areas of mathematics. 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 other topics.
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.
The book is suitable for advanced undergraduates, graduate students, and research mathematicians interested in differential geometry and neighboring fields, such as topology, harmonic analysis, and mathematical physics.
Advanced undergraduates, graduate students, and research mathematicians interested in differential geometry, topology, harmonic analysis, and mathematical physics.
Table of Contents
- Chapter 1. Lie groups
- Chapter 2. Maximal tori and the classification theorem
- Chapter 3. The geometry of a compact Lie group
- Chapter 4. Homogeneous spaces
- Chapter 5. The geometry of a reductive homogeneous space
- Chapter 6. Symmetric spaces
- Chapter 7. Generalized flag manifolds
- Chapter 8. Advanced topics