special orthogonal group SO(n)

URI: https://gptkb.org/entity/special_orthogonal_group_SO(n)

GPTKB entity

Statements (49)

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people gptkb:Lie_group
gptkbp:actsOn	gptkb:n-dimensional_Euclidean_space
gptkbp:application	gptkb:geometry computer vision mechanics physics robotics
gptkbp:centralTo	{I, -I} for even n, {I} for odd n
gptkbp:compact	true
gptkbp:consistsOf	n x n orthogonal matrices with determinant 1
gptkbp:definedIn	real numbers
gptkbp:dimensions	n(n-1)/2
gptkbp:fundamentalGroup	Z for n=2, Z_2 for n>2
gptkbp:generation	elementary rotations
gptkbp:hasConnection	true
gptkbp:hasSubgroup	gptkb:orthogonal_group_O(n)
https://www.w3.org/2000/01/rdf-schema#label	special orthogonal group SO(n)
gptkbp:identityElement	n x n identity matrix
gptkbp:isomorphicTo	rotation group in n dimensions
gptkbp:isSimple	true for n >= 5
gptkbp:notation	gptkb:SO(n)
gptkbp:order	infinite for n > 1
gptkbp:property	gptkb:Lie_group real algebraic group connected Lie group non-abelian for n > 2 semisimple for n >= 3
gptkbp:relatedTo	gptkb:general_linear_group_GL(n,_R) gptkb:Grassmannian_manifold gptkb:Stiefel_manifold gptkb:special_linear_group_SL(n,_R) gptkb:orthogonal_group_O(n) gptkb:special_unitary_group_SU(n) gptkb:Euclidean_group_E(n) gptkb:Lorentz_group_SO(1,_n-1) gptkb:orthogonal_group_O(n,_R) gptkb:projective_special_orthogonal_group_PSO(n) gptkb:rotation_group_SO(3) gptkb:special_linear_group_SL(n) gptkb:special_orthogonal_group_SO(2) gptkb:special_orthogonal_group_SO(4) orthogonal group orthogonal transformations rotation matrices spin group Spin(n)
gptkbp:universalCover	gptkb:Spin(n)
gptkbp:bfsParent	gptkb:Lie_group
gptkbp:bfsLayer	5