Lie algebra from Dynkin diagram

Here is the construction I gave in class for a Lie algebra given its Dynkin diagram.

Next will be some stuff about Weyl groups and Weyl chambers, delaying the fact that simple reflections generate N(T)/T.

We're going to do other chapters from here next, though in a different order: first the Bruhat decomposition, then stuff about Weyl chambers, filling the hole mentioned above, and then the Borel-Weil theorem that lets us construct all the irreps for complex reductive Lie groups.