Template:Dynkin/testcases
This is the template test cases page for the sandbox of Template:Dynkin. Script error: No such module "Purge". to update the examples. If there are many examples of a complicated template, later ones may break due to limits in MediaWiki, see the HTML comment "NewPP limit report" in the rendered page. You can also use Special:ExpandTemplates to examine the results of template uses. You can test how this page looks in the different skins with these links: |
Testing sandbox version
{{Dynkin/sandbox}}
Group name |
Dynkin diagram | Cartan matrix | Symmetry order |
Related simply-laced automorphic group3 | ||
---|---|---|---|---|---|---|
(Standard) multi-edged graph1 |
Valued graph2 |
<math>\left [\begin{matrix}2&a_{12}\\a_{21}&2\end{matrix}\right ]</math> | Determinant (4-a21*a12) | |||
Finite (Determinant>0) | ||||||
A1xA1 | Script error: No such module "Dynkin". Script error: No such module "Dynkin". | Script error: No such module "Dynkin". Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&0\\0&2\end{smallmatrix}\right ]</math> | 4 | 2 | |
A2 | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-1\\-1&2\end{smallmatrix}\right ]</math> | 3 | 3 | |
B2 | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-2\\-1&2\end{smallmatrix}\right ]</math> | 2 | 4 | <math>{A}_3</math> Script error: No such module "Dynkin". |
C2 | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-1\\-2&2\end{smallmatrix}\right ]</math> | 2 | 4 | <math>{A}_3</math> Script error: No such module "Dynkin". |
G2 | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-1\\-3&2\end{smallmatrix}\right ]</math> | 1 | 6 | <math>{D}_4</math> |
Affine (Determinant=0) | ||||||
A1(1) | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-2\\-2&2\end{smallmatrix}\right ]</math> | 0 | ∞ | <math>{\tilde{A}}_3</math> |
A2(2) | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-1\\-4&2\end{smallmatrix}\right ]</math> | 0 | ∞ | <math>{\tilde{D}}_4</math> |
Hyperbolic (Determinant<0) | ||||||
Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-1\\-5&2\end{smallmatrix}\right ]</math> | -1 | ∞ | H5(6) | ||
Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-b\\-a&2\end{smallmatrix}\right ]</math> | 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
{{Dynkin}}
Group name |
Dynkin diagram | Cartan matrix | Symmetry order |
Related simply-laced automorphic group3 | ||
---|---|---|---|---|---|---|
(Standard) multi-edged graph1 |
Valued graph2 |
<math>\left [\begin{matrix}2&a_{12}\\a_{21}&2\end{matrix}\right ]</math> | Determinant (4-a21*a12) | |||
Finite (Determinant>0) | ||||||
A1xA1 | Script error: No such module "Dynkin". Script error: No such module "Dynkin". | Script error: No such module "Dynkin". Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&0\\0&2\end{smallmatrix}\right ]</math> | 4 | 2 | |
A2 | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-1\\-1&2\end{smallmatrix}\right ]</math> | 3 | 3 | |
B2 | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-2\\-1&2\end{smallmatrix}\right ]</math> | 2 | 4 | <math>{A}_3</math> Script error: No such module "Dynkin". |
C2 | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-1\\-2&2\end{smallmatrix}\right ]</math> | 2 | 4 | <math>{A}_3</math> Script error: No such module "Dynkin". |
G2 | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-1\\-3&2\end{smallmatrix}\right ]</math> | 1 | 6 | <math>{D}_4</math> |
Affine (Determinant=0) | ||||||
A1(1) | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-2\\-2&2\end{smallmatrix}\right ]</math> | 0 | ∞ | <math>{\tilde{A}}_3</math> |
A2(2) | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-1\\-4&2\end{smallmatrix}\right ]</math> | 0 | ∞ | <math>{\tilde{D}}_4</math> |
Hyperbolic (Determinant<0) | ||||||
Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-1\\-5&2\end{smallmatrix}\right ]</math> | -1 | ∞ | H5(6) | ||
Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-b\\-a&2\end{smallmatrix}\right ]</math> | 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. |