1. Chapter 16 Lie Algebras Contents:
Tangent Space at the Identity of a Lie Group
The Tangent Space to SL(n,R) at I
The Tangent Space to O(n) at I
Left-Invariant Vector Fields on a Lie Group
The Lie Algebra of a Lie Group
The Lie Bracket on gl(n,R)
The Push-Forward of a Left-Invariant Vector Field
The Differential as a Lie Algebra Homomorphism
Problems

2. 16.1 Tangent Space at the Identity of a Lie Group

4. 16.2 The Tangent Space to SL(n,R) at I

6. 16.3 The Tangent Spaceto O(n) at I

8. 16.4 Left-Invariant Vector Fields on a Lie Group

15. 16.5 The Lie Algebra of a Lie Group

17. 16.6 The Lie Bracket on gl(n,R)

21. 16.7 The Push-Forward of a Left-Invariant Vector Field

25. 16.8 The Differential as a Lie Algebra Homomorphism

29. Problems

31. Hint:

33. Hint:

34. Hint:

38. Hint: