Support du graphe produit par l`algèbre de Lie partiellement

K
K
K

E F RE×F
G ⊆ E × F E=F
xRy y Rz⇒xRz
<
x < y ⇒y≮x
x≮x
6
x6y y 6x⇒y≮x
x6x
RER
E x y E x < y y < x
↔
(x↔y)⇔(y↔x)
x↔x
≡
(E, +)
+e1e2e3e4(E, +)
e1≡e2e3≡e4⇒e1+e3≡e2+e4

∼
(E, +) E
+
K
K
A
+
w x y z ∈ A
x+y∈ A
xy ∈ A
(x+y) + z=x+ (y+z)
0x+ 0 = 0 + x=x
x+−x=−x+x= 0
(xy)z=x(yz)
+ (w+x)(y+z) = (wy)+(wz)+(xy) +
(xz)
×
Kk∈K
k×x∈ A K
K
KLK
[,]L × L L
x y z ∈ L k∈K
[x+y, z] = [x, z]+[y, z]
[x, y +z] = [x, y]+[x, z]
[kx, y] = k[x, y]
[x, ky] = k[x, y]
[x, y] = −[y, x]
a, b, c ∈L(A, θ)
[a, [b, c]] + [c, [a, b]] + [b, [c, a]] = 0

A
A·
A∗(A∗,·)
θ(A∗,·)
(a, b)∈θ
v w (A∗,·)
v w θ
≡θt u v w ∈A∗
w≡θw w =w
v≡θw⇔w≡θv θ
v
u≡θv v ≡θw u ≡θw p1
u v p2v w
p3p1p2w u
·t≡θu v ≡θw t ·u≡θv·w
θ v
v θ θ(v)
A∗A∗
/≡θ
M(A, θ)
A=a, b, c θ = (a, b)
θ(aabcab) = aabcab, aabcba, abacab, abacba, baacab, baacba
(A∗
/≡θ,·)
T A∗
A∗
/≡θT T
A∗
/≡θ
w∈A∗
w=u1...un
i≤n ui