21 Mai

?
? G g
g2=eGG
? G H G
H G H
? G E
M(E, G)E G
G
E M(E, G)
G
E={1,2}M(E, G)
G×G
G M(E, G)
G=GLn(R)H=SLn(R)
H G
G/H
G, H, K φ :G→H
ψ:H→K
ψ◦φ
φ ψ ψ ◦φ
(ψ◦φ) = φ−1( (ψ))

φ ψ
ψ◦φ
?
x7→ φg(x) = gxg−1
(G)
(G)
Z(G)G G/Z(G)
(G)
? V n
GL(V)
V
GLn(R)
V
H K G
HK =G
H∩K={eG}
h∈H k ∈K hk =kh
G H ×K