|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
gptkb:Möbius_transformations
gptkb:Riemann_sphere
complex projective line
|
|
gptkbp:centerOfSL_2(C)
|
{±I}
|
|
gptkbp:compact
|
true
|
|
gptkbp:complexification
|
gptkb:PSL_2(C)
|
|
gptkbp:definedIn
|
SL_2(C) modulo its center
|
|
gptkbp:dimensions
|
3 complex dimensions
|
|
gptkbp:field
|
complex numbers
|
|
gptkbp:fullName
|
gptkb:Projective_Special_Linear_Group_of_2x2_matrices_over_the_complex_numbers
|
|
gptkbp:hasConnection
|
true
|
|
gptkbp:hasSubgroup
|
gptkb:PSL_2(R)
gptkb:PSL_2(Z)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
PSL 2(C)
|
|
gptkbp:isAlgebraicGroup
|
true
|
|
gptkbp:isClassicalGroup
|
true
|
|
gptkbp:isConnectedSimpleLieGroup
|
true
|
|
gptkbp:isLieGroupOver
|
complex numbers
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isNonCompactRealFormOf
|
gptkb:SL_2(C)
|
|
gptkbp:isNonCompactSimpleLieGroup
|
true
|
|
gptkbp:isomorphicTo
|
orientation-preserving isometry group of hyperbolic 3-space
|
|
gptkbp:isQuotientOf
|
gptkb:SL_2(C)
center of SL_2(C)
|
|
gptkbp:isReductive
|
true
|
|
gptkbp:isSemisimple
|
true
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:notation
|
gptkb:PSL(2,_C)
gptkb:PSL_2(C)
PSL₂(ℂ)
|
|
gptkbp:order
|
infinite
|
|
gptkbp:rank
|
1
|
|
gptkbp:realForm
|
gptkb:PSL_2(R)
|
|
gptkbp:relatedTo
|
gptkb:Fuchsian_groups
modular group
Kleinian groups
|
|
gptkbp:universalCover
|
PGL_2(C)
|
|
gptkbp:usedIn
|
gptkb:algebraic_geometry
gptkb:hyperbolic_geometry
complex analysis
3-manifold theory
theory of Riemann surfaces
|
|
gptkbp:bfsParent
|
gptkb:PSL_2(R)
gptkb:SL_2(C)
|
|
gptkbp:bfsLayer
|
8
|