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Special Orthogonal Group in 2 Dimensions
URI:
https://gptkb.org/entity/Special_Orthogonal_Group_in_2_Dimensions
GPTKB entity
Statements (47)
Predicate
Object
gptkbp:instanceOf
gptkb:group_of_people
gptkb:topology
gptkb:Lie_group
gptkbp:abbreviation
gptkb:SO(2)
gptkbp:application
gptkb:geometry
computer vision
crystallography
physics
robotics
gptkbp:centralTo
gptkb:SO(2)
gptkbp:compactSubgroupOf
gptkb:GL(2,_R)
gptkbp:containsElement
rotations in the plane
gptkbp:determinant
1
gptkbp:dimensions
1
gptkbp:fundamentalGroup
trivial
gptkbp:generation
skew-symmetric 2x2 matrix
gptkbp:groupOrder
infinite
gptkbp:homomorphismTo
gptkb:U(1)
gptkbp:homotopyType
gptkb:butter
https://www.w3.org/2000/01/rdf-schema#label
Special Orthogonal Group in 2 Dimensions
gptkbp:identityElement
transpose
2x2 identity matrix
gptkbp:isomorphicTo
gptkb:U(1)
gptkb:circle_group
gptkbp:Lie_algebra
so(2)
gptkbp:LieAlgebraDimension
1
gptkbp:matrixRepresentation
2x2 real orthogonal matrices with determinant 1
gptkbp:maximalTorusOf
gptkb:SO(3)
gptkbp:multiplication
matrix multiplication
gptkbp:orderOfElement
infinite
gptkbp:parameter
angle of rotation
gptkbp:relatedGroup
gptkb:Lie_group
simple
compact
orthogonal group
connected
abelian
gptkbp:relatedTo
gptkb:rotation_group
gptkb:SO(3)
gptkb:O(2)
orthogonal group
gptkbp:representationTheory
characters are e^{inθ}
gptkbp:structure
0
gptkbp:topology
circle topology
gptkbp:universalCover
real line (R)
gptkbp:bfsParent
gptkb:SO(2)
gptkbp:bfsLayer
7