- #1

BruceG

- 40

- 0

dimension of sl(2,C) = 2*(2*2-1) = 6, is isomorphic to so(3,1) : 3+2+1 = 6

dimension of sl(2,H) = 15, is isomorphic to so(5,1) : 5+4+3+2+1 = 15

dimension of sl(2,O) = 45, is isomorphic to so(9,1) : 9+8+7+6+5+4+3+2+1 = 45

How do you prove the 15 and 45?

Naively I would expect 4*(2*2-1)=12 and 8*(2*2-1)=24.