Can you see why the tori we have been using in SU(2) and SU(3) are maximal?

# Week 9

## Session 1

### Pre-class videos

### Pre-class exercises

Exercise:

Exercise:

Explicitly, what is the set of matrices \mathfrak{h}_{\ZZ} for our usual diagonal choice of maximal torus in SU(3)?

## Session 2

### Pre-class videos

### Pre-class exercises

Exercise:

Consider the basis of little s u 2 given by the *Pauli matrices* sigma_1 equals the matrix i, 0, 0, minus i; sigma_2 equals the matrix 0, 1, minus 1, 0; and sigma_3 equals the matrix 0, i, i, 0 Find all possible Killing dot products K(\sigma_i, \sigma_j).

## Optional extras