Orthogonal group of signature (1,n)

URI: https://gptkb.org/entity/Orthogonal_group_of_signature_(1,n)
GPTKB entity
Statements (32)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
gptkbp:actsOn real vector space of dimension n+1
gptkbp:alsoKnownAs O(1,n)
gptkbp:centralTo {±I} (for n>1)
gptkbp:compact true
gptkbp:dimensions (n+1)(n)/2
gptkbp:field gptkb:mathematics
gptkbp:hasComponent connected component SO^+(1,n)
gptkbp:hasConnectedComponent gptkb:identity_component_SO^+(1,n)
gptkbp:hasConnection false
gptkbp:hasDiscreteComponent O(1,n) \\ SO^+(1,n)
gptkbp:hasSubgroup general linear group GL(n+1, R)
special orthogonal group SO(1,n)
spin group Spin(1,n)
https://www.w3.org/2000/01/rdf-schema#label Orthogonal group of signature (1,n)
gptkbp:isMatrixGroup true
gptkbp:isReductive true
gptkbp:isSimple n>2
gptkbp:Lie_algebra so(1,n)
gptkbp:preserves quadratic form of signature (1,n)
Minkowski metric (for n=3)
bilinear form of signature (1,n)
gptkbp:realForm complex orthogonal group O(n+1, C)
gptkbp:relatedTo gptkb:Lorentz_group
pseudo-orthogonal group
gptkbp:usedIn gptkb:special_relativity
gptkb:hyperbolic_geometry
differential geometry
representation theory
theory of quadratic forms
gptkbp:bfsParent gptkb:Special_orthogonal_group_of_signature_(1,n)
gptkbp:bfsLayer 7