Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:centralTo |
{I, -I} if p+q+2 is even
{I} if p+q+2 is odd |
| gptkbp:compact |
true
|
| gptkbp:definedIn |
real numbers
|
| gptkbp:dimensions |
(p+q+2)(p+q+1)/2
|
| gptkbp:fullName |
Special orthogonal group of signature (p+1, q+1) over the real numbers
|
| gptkbp:hasConnection |
true for p+q+2 > 2
|
| gptkbp:hasSubgroup |
O(p+1,q+1; R)
|
| https://www.w3.org/2000/01/rdf-schema#label |
SO(p+1,q+1; R)
|
| gptkbp:isConnectedComponentOf |
O(p+1,q+1; R)
|
| gptkbp:isSimple |
true for p+q+2 > 2 except for low dimensions
|
| gptkbp:preserves |
quadratic form of signature (p+1, q+1)
|
| gptkbp:realForm |
SO(p+q+2; C)
|
| gptkbp:relatedGroup |
gptkb:group_of_people
|
| gptkbp:relatedTo |
gptkb:Lorentz_group
gptkb:conformal_group orthogonal group |
| gptkbp:usedIn |
gptkb:geometry
mathematical physics representation theory |
| gptkbp:bfsParent |
gptkb:SO(p+1,q+1)
|
| gptkbp:bfsLayer |
8
|