True or false: If we use a sub-maximal torus, is it still true that little h equals little g_0? If so, why? If not, what do we get instead?
Just by looking at the root diagrams, can you figure out the dimensions of the Lie algebras little s o 5 and little g 2?
Sketch the (3-dimensional) root system corresponding to your choice of Dynkin diagram from amongst: A_3, B_3, C_3 and D_3.