Statements (30)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:actsOn |
gptkb:n-sphere
(n+1)-dimensional real vector space |
| gptkbp:application |
gptkb:geometry
physics representation theory |
| gptkbp:centralTo |
{I, -I} for even n+1
{I} for odd n+1 |
| gptkbp:compact |
true
|
| gptkbp:defines |
Group of (n+1)×(n+1) orthogonal matrices with determinant 1
|
| gptkbp:dimensions |
(n+1)n/2
|
| gptkbp:field |
real numbers
|
| gptkbp:fullName |
gptkb:Special_orthogonal_group_in_n+1_dimensions
|
| gptkbp:fundamentalGroup |
ℤ/2ℤ for n+1 ≥ 3
|
| gptkbp:hasConnection |
true
|
| gptkbp:hasSubgroup |
gptkb:GL(n+1,_ℝ)
|
| gptkbp:isSimple |
true for n+1 ≥ 5
|
| gptkbp:Lie_algebra |
so(n+1)
|
| gptkbp:notation |
gptkb:SO(n+1,_ℝ)
|
| gptkbp:realForm |
gptkb:SO(n+1,_ℂ)
|
| gptkbp:relatedGroup |
gptkb:group_of_people
gptkb:orthogonal_group gptkb:rotation_group |
| gptkbp:relatedTo |
gptkb:Spin(n+1)
gptkb:SO(n) O(n+1) |
| gptkbp:universalCover |
gptkb:Spin(n+1)
|
| gptkbp:bfsParent |
gptkb:SO(1,n)
|
| gptkbp:bfsLayer |
6
|
| https://www.w3.org/2000/01/rdf-schema#label |
SO(n+1)
|