|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
gptkb:Riemann_sphere
complex projective line
hyperbolic 3-space
|
|
gptkbp:category
|
gptkb:semisimple_Lie_group
gptkb:Lie_group
|
|
gptkbp:centralTo
|
{±I}
|
|
gptkbp:defines
|
group of 2x2 complex matrices with determinant 1
|
|
gptkbp:determinant
|
1
|
|
gptkbp:dimensions
|
3 complex dimensions
6 real dimensions
|
|
gptkbp:field
|
ℂ
|
|
gptkbp:fullName
|
gptkb:Special_Linear_Group_of_2x2_complex_matrices
|
|
gptkbp:hasConnection
|
true
|
|
gptkbp:hasSubgroup
|
gptkb:SU(2)
gptkb:SL(2,_ℝ)
gptkb:GL(2,_ℂ)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(2, ℂ)
|
|
gptkbp:isDoubleCoverOf
|
gptkb:SO(3,1)^+
|
|
gptkbp:isomorphicTo
|
gptkb:Spin(3,1)
universal cover of the restricted Lorentz group
|
|
gptkbp:isQuotientOf
|
gptkb:PSL(2,_ℂ)
|
|
gptkbp:Lie_algebra
|
gptkb:sl(2,_ℂ)
|
|
gptkbp:matrixSize
|
2x2
|
|
gptkbp:notation
|
gptkb:SL(2,_C)
gptkb:SL_2(C)
|
|
gptkbp:order
|
infinite
|
|
gptkbp:rank
|
1
|
|
gptkbp:realForm
|
gptkb:SU(2)
gptkb:SL(2,_ℝ)
|
|
gptkbp:relatedGroup
|
simple
non-abelian
connected
non-compact
|
|
gptkbp:relatedTo
|
gptkb:Lorentz_group
projective linear group PSL(2, ℂ)
|
|
gptkbp:universalCover
|
gptkb:SO(3,1)^+
|
|
gptkbp:usedIn
|
gptkb:general_relativity
gptkb:quantum_field_theory
gptkb:hyperbolic_geometry
gptkb:theory_of_spinors
quantum mechanics
representation theory
theory of Riemann surfaces
theory of Möbius transformations
|
|
gptkbp:bfsParent
|
gptkb:SL(2,_C)
|
|
gptkbp:bfsLayer
|
7
|