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Testing sandbox version
edit{{Dynkin/sandbox}}
Group name |
Dynkin diagram | Cartan matrix | Symmetry order |
Related simply-laced automorphic group3 | ||
---|---|---|---|---|---|---|
(Standard) multi-edged graph1 |
Valued graph2 |
Determinant (4-a21*a12) | ||||
Finite (Determinant>0) | ||||||
A1xA1 | ![]() ![]() |
![]() ![]() |
4 | 2 | ||
A2 | ![]() ![]() ![]() |
![]() ![]() ![]() |
3 | 3 | ||
B2 | ![]() ![]() ![]() |
![]() ![]() ![]() |
2 | 4 | ![]() ![]() | |
C2 | ![]() ![]() ![]() |
![]() ![]() ![]() |
2 | 4 | ![]() ![]() | |
G2 | ![]() ![]() ![]() |
![]() ![]() ![]() |
1 | 6 | ![]() | |
Affine (Determinant=0) | ||||||
A1(1) | ![]() ![]() ![]() |
![]() ![]() ![]() |
0 | ∞ | ![]() | |
A2(2) | ![]() ![]() ![]() |
![]() ![]() ![]() |
0 | ∞ | ![]() | |
Hyperbolic (Determinant<0) | ||||||
![]() ![]() ![]() |
-1 | ∞ | H5(6) ![]() | |||
![]() ![]() ![]() |
4-ab | ∞ | ||||
Note1: The multi-edged diagram corresponds to the nondiagonal Cartan matrix elements a21, a12, with the number of edges drawn equal to max(a21, a12), and an arrow pointing towards nonunity element(s). Note2: For hyperbolic groups, (a12*a21>4), the multiedge style is abandoned in favor of an explicit labeling (a21, a12) on the edge. These are usually not applied to finite and affine graphs. Note3: Many multi-edged groups are automorphic via a folding operation with a higher ranked simply-laced group. |
Testing main template
edit{{Dynkin}}
Group name |
Dynkin diagram | Cartan matrix | Symmetry order |
Related simply-laced automorphic group3 | ||
---|---|---|---|---|---|---|
(Standard) multi-edged graph1 |
Valued graph2 |
Determinant (4-a21*a12) | ||||
Finite (Determinant>0) | ||||||
A1xA1 | ![]() ![]() |
![]() ![]() |
4 | 2 | ||
A2 | ![]() ![]() ![]() |
![]() ![]() ![]() |
3 | 3 | ||
B2 | ![]() ![]() ![]() |
![]() ![]() ![]() |
2 | 4 | ![]() ![]() | |
C2 | ![]() ![]() ![]() |
![]() ![]() ![]() |
2 | 4 | ![]() ![]() | |
G2 | ![]() ![]() ![]() |
![]() ![]() ![]() |
1 | 6 | ![]() | |
Affine (Determinant=0) | ||||||
A1(1) | ![]() ![]() ![]() |
![]() ![]() ![]() |
0 | ∞ | ![]() | |
A2(2) | ![]() ![]() ![]() |
![]() ![]() ![]() |
0 | ∞ | ![]() | |
Hyperbolic (Determinant<0) | ||||||
![]() ![]() ![]() |
-1 | ∞ | H5(6) ![]() | |||
![]() ![]() ![]() |
4-ab | ∞ | ||||
Note1: The multi-edged diagram corresponds to the nondiagonal Cartan matrix elements a21, a12, with the number of edges drawn equal to max(a21, a12), and an arrow pointing towards nonunity element(s). Note2: For hyperbolic groups, (a12*a21>4), the multiedge style is abandoned in favor of an explicit labeling (a21, a12) on the edge. These are usually not applied to finite and affine graphs. Note3: Many multi-edged groups are automorphic via a folding operation with a higher ranked simply-laced group. |