|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
gptkb:Riemann_sphere
complex projective line
hyperbolic 3-space
|
|
gptkbp:centralTo
|
{±I}
|
|
gptkbp:compact
|
true
|
|
gptkbp:complexification
|
gptkb:SL(2,ℝ)
|
|
gptkbp:connects
|
true
|
|
gptkbp:defines
|
group of 2x2 complex matrices with determinant 1
|
|
gptkbp:determinant
|
1
|
|
gptkbp:dimensions
|
3
|
|
gptkbp:field
|
complex numbers
|
|
gptkbp:fullName
|
gptkb:Special_Linear_Group_of_2x2_Complex_Matrices
|
|
gptkbp:generatorCount
|
3
|
|
gptkbp:hasConnection
|
true
|
|
gptkbp:hasSubgroup
|
gptkb:Weyl_group
gptkb:SL(2,ℝ)
gptkb:SU(2)
gptkb:maximal_torus
Borel subgroup
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(2,ℂ)
|
|
gptkbp:isAlgebraicGroup
|
true
|
|
gptkbp:isComplexLieGroup
|
true
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isPerfect
|
true
|
|
gptkbp:isQuotientOf
|
gptkb:PSL(2,ℂ)
|
|
gptkbp:isReductive
|
true
|
|
gptkbp:isSemisimple
|
true
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:isSpecialLinearGroup
|
true
|
|
gptkbp:isUnimodular
|
true
|
|
gptkbp:Lie_algebra
|
sl(2,ℂ)
|
|
gptkbp:rank
|
1
|
|
gptkbp:realForm
|
gptkb:SL(2,ℝ)
|
|
gptkbp:relatedGroup
|
non-compact
|
|
gptkbp:relatedTo
|
gptkb:Lorentz_group
gptkb:SU(2)
gptkb:PSL(2,ℂ)
|
|
gptkbp:simplyConnected
|
true
|
|
gptkbp:universalCover
|
gptkb:SO(3,1)^+
|
|
gptkbp:usedIn
|
gptkb:geometry
gptkb:special_relativity
gptkb:theoretical_physics
quantum mechanics
representation theory
|
|
gptkbp:bfsParent
|
gptkb:SL(2,ℝ)
|
|
gptkbp:bfsLayer
|
6
|