Simplicité de SO 3 FGN 3 algèbre page 67

SO3
G SO3G
SO(3)
ΠSO3SO3
g∈G g G(g)
G G0
So3h θ
Id h tθ ht
htgh−1
tg hgh−1g hgh−1
G(Id) := G0G
g h G0γ γ0
g Id h Id G γ00 =γγ0−1
G g 7→ g−1
GL γ00 gh−1
G0
G0G
g h
γ γ(t)h−1gh−1
g=h G g
So3h g hgh−1g=hgh−1
gh =hg SO3g=Id
G=So3G0
θ cos(θ) = (tr(g)−1)/2
g
0G π/2r
r2π
Id 0 1
G
+−π/2