|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:actsOn
|
gptkb:projective_line_over_R
upper half-plane
|
|
gptkbp:centralTo
|
{±I}
|
|
gptkbp:defines
|
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:fundamentalGroup
|
Z
|
|
gptkbp:hasCartanDecomposition
|
true
|
|
gptkbp:hasConnection
|
false
true
|
|
gptkbp:hasDiscreteSeriesRepresentations
|
true
|
|
gptkbp:hasDiscreteSubgroup
|
gptkb:modular_group
|
|
gptkbp:hasIwasawaDecomposition
|
true
|
|
gptkbp:hasMaximalSubgroup
|
gptkb:SO(2)
|
|
gptkbp:hasSubgroup
|
gptkb:SO(2)
gptkb:SL_2(Z)
Borel subgroup
maximal compact subgroup
|
|
gptkbp:isDoubleCoverOf
|
gptkb:PSL_2(R)
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isQuotientOf
|
gptkb:PSL_2(R)
|
|
gptkbp:isReductive
|
true
|
|
gptkbp:isSemisimple
|
true
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:Lie_algebra
|
sl_2(R)
|
|
gptkbp:notation
|
gptkb:SL_2(R)
|
|
gptkbp:order
|
infinite
|
|
gptkbp:realForm
|
gptkb:SL_2(C)
|
|
gptkbp:realRank
|
1
|
|
gptkbp:relatedGroup
|
gptkb:group_of_people
gptkb:Lie_group
non-compact Lie group
|
|
gptkbp:relatedTo
|
gptkb:PSL_2(R)
gptkb:SL_2(C)
gptkb:SL_2(Q)
gptkb:SL_2(Z)
|
|
gptkbp:type
|
A1
|
|
gptkbp:universalCover
|
universal covering group of SL_2(R)
|
|
gptkbp:usedIn
|
gptkb:hyperbolic_geometry
differential geometry
modular forms
number theory
representation theory
automorphic forms
theory of Riemann surfaces
|
|
gptkbp:bfsParent
|
gptkb:Serge_Lang
|
|
gptkbp:bfsLayer
|
6
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL 2(R)
|