Structure and Geometry of Lie Groups

1. Introduction
Joachim Hilgert, Karl-Hermann Neeb

2. Concrete Matrix Groups
Joachim Hilgert, Karl-Hermann Neeb

3. The Matrix Exponential Function
Joachim Hilgert, Karl-Hermann Neeb

4. Linear Lie Groups
Joachim Hilgert, Karl-Hermann Neeb

5. Elementary Structure Theory of Lie Algebras
Joachim Hilgert, Karl-Hermann Neeb

6. Root Decomposition
Joachim Hilgert, Karl-Hermann Neeb

7. Representation Theory of Lie Algebras
Joachim Hilgert, Karl-Hermann Neeb

8. Smooth Manifolds
Joachim Hilgert, Karl-Hermann Neeb

9. Basic Lie Theory
Joachim Hilgert, Karl-Hermann Neeb

10. Smooth Actions of Lie Groups
Joachim Hilgert, Karl-Hermann Neeb

11. Normal Subgroups, Nilpotent and Solvable Lie Groups
Joachim Hilgert, Karl-Hermann Neeb

12. Compact Lie Groups
Joachim Hilgert, Karl-Hermann Neeb

13. Semisimple Lie Groups
Joachim Hilgert, Karl-Hermann Neeb

14. General Structure Theory
Joachim Hilgert, Karl-Hermann Neeb

15. Complex Lie Groups
Joachim Hilgert, Karl-Hermann Neeb

16. Linearity of Lie Groups
Joachim Hilgert, Karl-Hermann Neeb

17. Classical Lie Groups
Joachim Hilgert, Karl-Hermann Neeb

18. Nonconnected Lie Groups
Joachim Hilgert, Karl-Hermann Neeb

Keywords: Mathematics, Topological Groups, Lie Groups, Differential Geometry, Algebraic Topology, Algebra