Contents
Preface ix
Introduction xi
Chapter 1. Lie Groups 1
1. An example of a Lie group 1
2. Smooth manifolds: A review 2
3. Lie groups 8
4. The tangent space of a Lie group - Lie algebras 12
5. One-parameter subgroups 15
6. The Campbell-Baker-HausdorfT formula 20
7. Lie's theorems 21
Chapter 2. Maximal Tori and the Classification Theorem 23
1. Representation theory: elementary concepts 24
2. The adjoint representation 28
3. The Killing form 32
4. Maximal tori 36
5. The classification of compact and connected Lie
groups 39
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