|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
gptkb:Riemann_sphere
complex projective line
|
|
gptkbp:centralTo
|
{±I}
|
|
gptkbp:compact
|
true
|
|
gptkbp:complexification
|
gptkb:SU(2)
gptkb:SL(2,_R)
|
|
gptkbp:defines
|
group of 2x2 complex matrices with determinant 1
|
|
gptkbp:dimensions
|
6
|
|
gptkbp:field
|
complex numbers
|
|
gptkbp:fullName
|
gptkb:Special_Linear_Group_of_2x2_complex_matrices
|
|
gptkbp:fundamentalGroup
|
trivial
|
|
gptkbp:hasConnection
|
true
|
|
gptkbp:hasSubgroup
|
gptkb:SU(2)
gptkb:SL(2,_R)
gptkb:maximal_torus
Borel subgroup
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(2, C)
|
|
gptkbp:isAlgebraicGroup
|
true
|
|
gptkbp:isDoubleCoverOf
|
gptkb:SO(3,1)^+
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isNonCompactRealFormOf
|
gptkb:SL(2,_C)
|
|
gptkbp:isQuotientOf
|
gptkb:PSL(2,_C)
|
|
gptkbp:isReductive
|
true
|
|
gptkbp:isSemisimple
|
true
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:Lie_algebra
|
gptkb:sl(2,_C)
|
|
gptkbp:notation
|
gptkb:SL(2,_ℂ)
|
|
gptkbp:realForm
|
gptkb:SL(2,_R)
|
|
gptkbp:relatedTo
|
gptkb:projective_linear_group_PGL(2,_C)
gptkb:Lorentz_group
gptkb:conformal_group
|
|
gptkbp:universalCover
|
gptkb:PSL(2,_C)
gptkb:SO(3,1)^+
|
|
gptkbp:usedIn
|
gptkb:algebraic_geometry
gptkb:hyperbolic_geometry
gptkb:theory_of_spinors
mathematical physics
quantum mechanics
representation theory
theory of automorphic forms
theory of 3-manifolds
theory of Möbius transformations
theory of discrete groups
|
|
gptkbp:bfsParent
|
gptkb:SL2
|
|
gptkbp:bfsLayer
|
6
|