Matrix Groups: Part 14

Covers pages 39 to 40 of my notes. Lie algebra of the tori are detailed. Further detail on the conjugates of tori are also given as to place regular elements on just one such torus. Finally, the classification of compact matrix groups is given. We explain that all there is to find is direct products of SO(n), SU(n), Sp(n) and the 5 exceptional Lie groups. Of course, these results are due to an entirely different course of study. See Erdmann and Wildon's "Introduction to Lie Algebras" for a treatment which is essentially at the same level as Tapp.