True or false: If we use a sub-maximal torus, is it still true that $\U0001d525={\U0001d524}_{0}$ ? If so, why? If not, what do we get instead?

# Week 10

## Session 1

### Pre-class videos

### Pre-class exercises

Exercise:

## Session 2

### Pre-class videos

### Pre-class exercises

Exercise:

Just by looking at the root diagrams, can you figure out the dimensions of the Lie algebras $\U0001d530\U0001d52c(5)$ and ${\U0001d524}_{2}$ ?

Exercise:

Sketch the (3-dimensional) root system corresponding to your choice of Dynkin diagram from amongst: ${A}_{3}$ , ${B}_{3}$ , ${C}_{3}$ and ${D}_{3}$ .

## Optional extras