|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
gptkb:projective_line_over_ℝ
upper half-plane
|
|
gptkbp:centralTo
|
{±I}
|
|
gptkbp:compact
|
yes
|
|
gptkbp:defines
|
The group of 2x2 real matrices with determinant 1
|
|
gptkbp:dimensions
|
3
|
|
gptkbp:field
|
ℝ
|
|
gptkbp:fullName
|
gptkb:Special_Linear_Group_of_2x2_real_matrices
|
|
gptkbp:hasConnection
|
yes
|
|
gptkbp:hasDiscreteSubgroup
|
gptkb:SL(2,ℤ)
modular group
|
|
gptkbp:hasSubgroup
|
gptkb:SO(2)
diagonal matrices with determinant 1
upper triangular matrices with determinant 1
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(2,ℝ)
|
|
gptkbp:isNonAbelian
|
yes
|
|
gptkbp:isQuotientOf
|
gptkb:PSL(2,ℝ)
|
|
gptkbp:isSimple
|
yes
|
|
gptkbp:Lie_algebra
|
gptkb:sl(2,ℝ)
|
|
gptkbp:maximalCompactSubgroup
|
gptkb:SO(2)
|
|
gptkbp:notation
|
gptkb:SL(2,ℝ)
|
|
gptkbp:order
|
infinite
|
|
gptkbp:rank
|
1
|
|
gptkbp:realForm
|
gptkb:SL(2,ℂ)
|
|
gptkbp:relatedGroup
|
simple
non-abelian
connected
non-compact
|
|
gptkbp:relatedTo
|
gptkb:hyperbolic_geometry
gptkb:Lorentz_group
gptkb:Fuchsian_groups
modular forms
representation theory
automorphic forms
modular group
orthogonal group
|
|
gptkbp:universalCover
|
gptkb:universal_covering_group_of_SL(2,ℝ)
|
|
gptkbp:bfsParent
|
gptkb:modular_group
|
|
gptkbp:bfsLayer
|
5
|