Statements (30)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:actsOn |
N-dimensional real vector space
|
| gptkbp:application |
gptkb:geometry
computer vision physics robotics |
| gptkbp:centralTo |
{I} for odd N, {I, -I} for even N
|
| gptkbp:compact |
true
|
| gptkbp:connects |
true
|
| gptkbp:containsElement |
N x N orthogonal matrices with determinant 1
|
| gptkbp:determinant |
1
|
| gptkbp:dimensions |
N(N-1)/2
|
| gptkbp:field |
real numbers
|
| gptkbp:fullName |
gptkb:Special_Orthogonal_Group_in_N_dimensions
|
| gptkbp:fundamentalGroup |
Z for N=2, Z_2 for N>2
|
| gptkbp:generation |
antisymmetric matrices
|
| gptkbp:hasSubgroup |
O(N)
|
| gptkbp:homogeneousSpace |
gptkb:sphere_S^{N-1}
|
| gptkbp:isomorphicTo |
SU(2) for SO(3)
U(1) for SO(2) |
| gptkbp:isSimple |
N ≥ 5
|
| gptkbp:Lie_algebra |
so(N)
|
| gptkbp:maximalTorus |
rank floor(N/2)
|
| gptkbp:notation |
gptkb:SO(N,_ℝ)
|
| gptkbp:relatedGroup |
gptkb:orthogonal_group
gptkb:rotation_group |
| gptkbp:relatedTo |
conservation of angular momentum
rotation symmetry |
| https://www.w3.org/2000/01/rdf-schema#label |
SO(N)
|