special orthogonal group SO(2)

URI: https://gptkb.org/entity/special_orthogonal_group_SO(2)
GPTKB entity
Statements (34)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
gptkb:topology
gptkb:Lie_group
gptkbp:actsOn Euclidean plane
gptkbp:centralTo gptkb:SO(2)
gptkbp:compact true
gptkbp:connects true
gptkbp:containsElement 2x2 real orthogonal matrices with determinant 1
gptkbp:determinant 1
gptkbp:dimensions 1
gptkbp:field real numbers
gptkbp:fundamentalGroup Z (integers)
gptkbp:generation rotation matrix
gptkbp:hasSubgroup general linear group GL(2, R)
orthogonal group O(2)
special orthogonal group SO(3)
gptkbp:homotopyType circle S^1
https://www.w3.org/2000/01/rdf-schema#label special orthogonal group SO(2)
gptkbp:identityElement 2x2 identity matrix
gptkbp:isNonAbelian true
gptkbp:isomorphicTo circle group U(1)
gptkbp:isSimple false
gptkbp:Lie_algebra so(2)
gptkbp:LieAlgebraDimension 1
gptkbp:namedAfter orthogonal matrices
gptkbp:notation gptkb:SO(2)
gptkbp:order infinite
gptkbp:parameter angle theta
gptkbp:realization matrices of the form [[cos θ, -sin θ], [sin θ, cos θ]]
gptkbp:representationTheory all irreducible representations are 1-dimensional
gptkbp:represents rotations in the plane
gptkbp:universalCover gptkb:real_line_R
gptkbp:bfsParent gptkb:special_orthogonal_group_SO(n)
gptkbp:bfsLayer 6