Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Weyl_group
|
| gptkbp:actsOn |
gptkb:n-dimensional_Euclidean_space
|
| gptkbp:appearsIn |
algebraic group theory
Lie algebra theory |
| gptkbp:associatedWith |
root system of type D_n
|
| gptkbp:CoxeterGroupType |
D_n
|
| gptkbp:Dynkin_diagram |
gptkb:D_n_diagram
|
| gptkbp:generation |
reflections
|
| gptkbp:hasOrderFormula |
2^{n-1} n!
|
| gptkbp:hasSubgroup |
Weyl group of type B_n
|
| https://www.w3.org/2000/01/rdf-schema#label |
Weyl group of type D n
|
| gptkbp:isFinite |
true
|
| gptkbp:isomorphicTo |
gptkb:even_signed_permutation_group
|
| gptkbp:isSimple |
n ≥ 4, except n=4 (not simple)
|
| gptkbp:order |
2^{n-1} n!
|
| gptkbp:presentedBy |
Coxeter presentation with D_n relations
|
| gptkbp:relatedTo |
Spin group Spin(2n)
special orthogonal group SO(2n) |
| gptkbp:bfsParent |
gptkb:D_n_root_lattice
|
| gptkbp:bfsLayer |
6
|