- #1
BruceG
- 40
- 0
dimension of sl(2,R) = 1*(2*2-1) = 3, is isomorphic to so(2,1) : 2+1 = 3
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.
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.