Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:actsOn |
R^{p+q+2}
|
| gptkbp:centralTo |
{I, -I} if p+q+2 is even
{I} if p+q+2 is odd |
| gptkbp:connectedComponent |
gptkb:SO^0(p+1,q+1)
|
| gptkbp:determinant |
1
|
| gptkbp:dimensions |
(p+q+2)(p+q+1)/2
|
| gptkbp:fullName |
Special orthogonal group of signature (p+1,q+1)
|
| gptkbp:hasSubgroup |
gptkb:O(p+1,q+1)
|
| https://www.w3.org/2000/01/rdf-schema#label |
SO(p+1,q+1)
|
| gptkbp:isSimple |
true for p+q+2 > 2
|
| gptkbp:notation |
gptkb:SO(p+1,q+1;_R)
|
| gptkbp:preserves |
quadratic form of signature (p+1,q+1)
|
| gptkbp:relatedGroup |
gptkb:group_of_people
gptkb:Lie_group orthogonal group |
| gptkbp:relatedTo |
gptkb:Lorentz_group_for_p=1,_q=2
conformal group in (p,q) dimensions spin group Spin(p+1,q+1) |
| gptkbp:bfsParent |
gptkb:conformal_group
|
| gptkbp:bfsLayer |
7
|