|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
gptkb:Riemann_sphere
complex projective line
|
|
gptkbp:centralTo
|
{±I}
|
|
gptkbp:definedIn
|
group of 2x2 complex matrices with determinant 1
|
|
gptkbp:dimensions
|
3 complex dimensions
6 real dimensions
|
|
gptkbp:field
|
complex numbers
|
|
gptkbp:fullName
|
gptkb:Special_Linear_Group_of_2x2_Complex_Matrices
|
|
gptkbp:generation
|
elementary matrices
|
|
gptkbp:hasProperty
|
gptkb:Lie_group
non-abelian
connected
simply connected
non-compact
reductive
semisimple
|
|
gptkbp:hasSubgroup
|
gptkb:SU(2)
gptkb:SL(2,R)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(2,C)
|
|
gptkbp:isomorphicTo
|
gptkb:Spin(3,1)
|
|
gptkbp:isQuotientOf
|
gptkb:PSL(2,C)
|
|
gptkbp:Lie_algebra
|
gptkb:sl(2,C)
|
|
gptkbp:notation
|
gptkb:SL(2,ℂ)
|
|
gptkbp:order
|
infinite
|
|
gptkbp:relatedGroup
|
simple
non-abelian
connected
non-compact
|
|
gptkbp:relatedTo
|
gptkb:projective_linear_group_PSL(2,C)
gptkb:Lorentz_group
orthogonal group
|
|
gptkbp:universalCover
|
gptkb:SO(3,1)^+
|
|
gptkbp:usedIn
|
gptkb:theory_of_special_relativity
gptkb:algebraic_geometry
gptkb:quantum_field_theory
gptkb:hyperbolic_geometry
quantum mechanics
representation theory
knot theory
theory of Möbius transformations
|
|
gptkbp:bfsParent
|
gptkb:洛伦兹群
gptkb:Lorentz_group
|
|
gptkbp:bfsLayer
|
6
|