### 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.

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.