Lie Groups /
This book is a (post)graduate textbook on Lie groups and Lie algebras. Its aim is to give a broad introduction to the field with an emphasis on using differential-geometrical methods, in the spirit of Lie himself. The structure of compact Lie groups is analyzed in terms of the action of the group on...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg :
Springer Berlin Heidelberg,
2000.
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| Series: | Universitext,
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| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Preface
- Lie Groups and Lie Algebras: Lie Groups and their Lie Algebras; Examples; The Exponential Map; The Exponential Map for a Vector Space; The Tangent Map of Exp; The Product in Logarithmic Coordinates; Dynkin's Formula; Lie's Fundamental Theorems; The Component of the Identity; Lie Subgroups and Homomorphisms; Quotients; Connected Commutative Lie Groups; Simply Connected Lie Groups; Lie's Third Fundamental Theorem in Global Form; Exercises
- Proper Actions: Review; Bochner's Linearization Theorem; Slices; Associated Fiber Bundles; Smooth Functions on the Orbit Space; Orbit Types and Local Action Types; The Stratification by Orbit Types; Principal and Regular Orbits; Blowing Up
- Compact Lie Groups: Centralizers; The Adjoint Action; Connectedness of Centralizers; The Group of Rotations and its Covering Group; ... Representations of Compact Groups: ... Schur's Lemma; Averaging; The Peter-Weyl Theorem; ... Weight Exercises; The Borel-Weil Theorem ...
- Appendix.