Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:actsOn |
(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:connects |
true
|
| gptkbp:definedIn |
ℝ
|
| gptkbp:determinant |
1
|
| gptkbp:dimensions |
(n+1)n/2
|
| gptkbp:fullName |
Special orthogonal group of degree n+1 over the real numbers
|
| gptkbp:fundamentalGroup |
ℤ₂ (for n+1 ≥ 3)
|
| gptkbp:hasSubgroup |
gptkb:GL(n+1,_ℝ)
O(n+1, ℝ) |
| https://www.w3.org/2000/01/rdf-schema#label |
SO(n+1, ℝ)
|
| gptkbp:isSimple |
n+1 ≥ 3
|
| gptkbp:Lie_algebra |
so(n+1, ℝ)
|
| gptkbp:matrixCondition |
A^T A = I
det(A) = 1 |
| gptkbp:maximalCompactSubgroupOf |
gptkb:SO(n+1,_ℂ)
|
| gptkbp:preserves |
gptkb:Euclidean_inner_product
|
| gptkbp:relatedGroup |
gptkb:group_of_people
orthogonal group |
| gptkbp:relatedTo |
gptkb:rotation_group
symmetry group of the n-sphere |
| gptkbp:bfsParent |
gptkb:SO(n+1)
|
| gptkbp:bfsLayer |
7
|