Special Orthogonal Group in 2 Dimensions

GPTKB entity

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
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 gptkb:orthogonal_group simple compact connected abelian
gptkbp:relatedTo	gptkb:orthogonal_group gptkb:rotation_group gptkb:SO(3) gptkb:O(2)
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
https://www.w3.org/2000/01/rdf-schema#label	Special Orthogonal Group in 2 Dimensions