|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
upper half-plane
projective line
|
|
gptkbp:centralTo
|
{±I}
|
|
gptkbp:compact
|
yes
|
|
gptkbp:defines
|
The group of 2x2 real matrices with determinant 1
|
|
gptkbp:determinant
|
1
|
|
gptkbp:dimensions
|
3
|
|
gptkbp:field
|
ℝ
|
|
gptkbp:fullName
|
gptkb:Special_Linear_Group_of_2x2_real_matrices
|
|
gptkbp:fundamentalGroup
|
ℤ
|
|
gptkbp:groupOrder
|
infinite
|
|
gptkbp:hasBorelSubgroup
|
yes
|
|
gptkbp:hasCartanDecomposition
|
yes
|
|
gptkbp:hasConnection
|
yes
|
|
gptkbp:hasDiscreteSubgroup
|
modular group
|
|
gptkbp:hasIwasawaDecomposition
|
yes
|
|
gptkbp:hasMaximalSubgroup
|
gptkb:SO(2)
|
|
gptkbp:hasParabolicSubgroup
|
yes
|
|
gptkbp:hasSubgroup
|
gptkb:SO(2)
GL(2, ℝ)
PSL(2, ℝ)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(2, ℝ)
|
|
gptkbp:isMatrixGroup
|
yes
|
|
gptkbp:isNonAbelian
|
yes
|
|
gptkbp:isRealGroup
|
yes
|
|
gptkbp:isReductive
|
yes
|
|
gptkbp:isSemisimple
|
yes
|
|
gptkbp:isSimple
|
yes
|
|
gptkbp:isSimpleConnected
|
no
|
|
gptkbp:isTopologicalGroup
|
yes
|
|
gptkbp:Lie_algebra
|
sl(2, ℝ)
|
|
gptkbp:rank
|
1
|
|
gptkbp:realForm
|
gptkb:SL(2,_ℂ)
|
|
gptkbp:relatedTo
|
gptkb:SU(2)
modular group
PSL(2, ℝ)
|
|
gptkbp:universalCover
|
universal covering group of SL(2, ℝ)
|
|
gptkbp:usedIn
|
gptkb:hyperbolic_geometry
differential geometry
modular forms
number theory
representation theory
automorphic forms
|
|
gptkbp:bfsParent
|
gptkb:SL(2,_R)
gptkb:SL(2,_ℤ)
|
|
gptkbp:bfsLayer
|
7
|