|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
gptkb:3-dimensional_Euclidean_space
|
|
gptkbp:application
|
computer graphics
crystallography
physics
robotics
|
|
gptkbp:centralTo
|
trivial group
|
|
gptkbp:compact
|
true
|
|
gptkbp:connects
|
true
|
|
gptkbp:containsElement
|
3x3 orthogonal matrices with determinant 1
|
|
gptkbp:definedIn
|
real numbers
|
|
gptkbp:dimensions
|
3
|
|
gptkbp:discoveredBy
|
gptkb:Sophus_Lie
|
|
gptkbp:fullName
|
special orthogonal group in 3 dimensions
|
|
gptkbp:fundamentalGroup
|
cyclic group of order 2
|
|
gptkbp:generation
|
rotations about coordinate axes
|
|
gptkbp:hasSubgroup
|
gptkb:orthogonal_group_O(3)
|
|
gptkbp:homogeneousSpace
|
sphere S2
|
|
gptkbp:homotopyGroup
|
π1(SO(3)) = Z2
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
rotation group SO(3)
|
|
gptkbp:identityElement
|
3x3 identity matrix
|
|
gptkbp:irreducibleRepresentation
|
spherical harmonics
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isomorphicTo
|
SO(3) ≅ SU(2)/Z2
|
|
gptkbp:isQuotientOf
|
O(3)/SO(3) is isomorphic to Z2
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:Lie_algebra
|
so(3)
|
|
gptkbp:maximalTorus
|
gptkb:SO(2)
|
|
gptkbp:notation
|
gptkb:SO(3)
|
|
gptkbp:operator
|
matrix multiplication
|
|
gptkbp:order
|
infinite
|
|
gptkbp:realRank
|
1
|
|
gptkbp:relatedTo
|
gptkb:Euler_angles
gptkb:orthogonal_group_O(3)
quaternions
rotation matrices
|
|
gptkbp:universalCover
|
gptkb:SU(2)
|
|
gptkbp:bfsParent
|
gptkb:special_orthogonal_group_SO(n)
|
|
gptkbp:bfsLayer
|
6
|