|
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}
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SO(N)
|
|
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:rotation_group
orthogonal group
|
|
gptkbp:relatedTo
|
conservation of angular momentum
rotation symmetry
|
|
gptkbp:bfsParent
|
gptkb:gauge_theory
|
|
gptkbp:bfsLayer
|
5
|