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Template:Dynkin/testcases

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Testing sandbox version

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{{Dynkin/sandbox}}


Rank 2 Dynkin diagrams
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}}


Rank 2 Dynkin diagrams
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.