Special orthogonal group of signature (1,n)
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:actsOn |
gptkb:n-dimensional_hyperbolic_space
|
| gptkbp:alsoKnownAs |
gptkb:SO(1,n)
|
| gptkbp:compact |
true
|
| gptkbp:dimensions |
n(n+1)/2
|
| gptkbp:hasComponent |
gptkb:identity_component_SO^+(1,n)
|
| gptkbp:hasConnection |
false
|
| gptkbp:hasSubgroup |
gptkb:Orthogonal_group_of_signature_(1,n)
General linear group |
| https://www.w3.org/2000/01/rdf-schema#label |
Special orthogonal group of signature (1,n)
|
| gptkbp:isReductive |
true
|
| gptkbp:isSimple |
true (for n > 2)
|
| gptkbp:Lie_algebra |
so(1,n)
|
| gptkbp:notation |
gptkb:SO(1,n)
|
| gptkbp:preserves |
quadratic form of signature (1,n)
|
| gptkbp:realForm |
gptkb:Special_orthogonal_group_over_complex_numbers
|
| gptkbp:relatedTo |
gptkb:hyperbolic_geometry
gptkb:Lorentz_group pseudo-Riemannian geometry |
| gptkbp:universalCover |
gptkb:Spin(1,n)
|
| gptkbp:bfsParent |
gptkb:SO(1,n)
|
| gptkbp:bfsLayer |
6
|