Week 2

Session 1

Pre-class videos 40.59

The Lie algebra of a matrix group, accessible version 15.45
Example: O(n), accessible version 11.57
Example: SL(2,C), accessible version 13.17

Pre-class exercises

Exercise:

Prove that if X and Y are in little o n then X bracket Y is also in little o n.

Exercise:

Show that X equals 0, 1; 0, 0 and Y equals 0, 0; 1, 0 are in little s l 2 C.

Session 2

Pre-class videos 35.47

Lie algebras, accessible version 8.36
Lie algebra as a tangent space, accessible version 14.36
Proof that little g is a Lie algebra, accessible version 12.35

Pre-class exercises

Exercise:

Check that the Jacobi identity holds for the commutator bracket X bracket Y equals X Y minus Y X.

Exercise:

Why is the tangent vector to exp of s X at s = 0 equal to X?

Additional

Local coordinates, accessible version 26.34