Statements (30)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:actsOn |
gptkb:hyperbolic_plane
upper half-plane |
| gptkbp:centerOfSL(2,ℝ) |
{±I}
|
| gptkbp:compact |
true
|
| gptkbp:definedIn |
SL(2,ℝ) modulo its center
|
| gptkbp:dimensions |
3
|
| gptkbp:fullName |
gptkb:Projective_Special_Linear_Group_of_2x2_real_matrices
|
| gptkbp:hasConnection |
true
|
| gptkbp:hasDiscreteSubgroup |
modular group
|
| https://www.w3.org/2000/01/rdf-schema#label |
PSL(2,ℝ)
|
| gptkbp:isLocallyIsomorphicTo |
gptkb:SL(2,ℝ)
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isomorphicTo |
orientation-preserving isometries of the hyperbolic plane
|
| gptkbp:isQuotientOf |
gptkb:SL(2,ℝ)
|
| gptkbp:isRealRank |
1
|
| gptkbp:isSimple |
true
|
| gptkbp:Lie_algebra |
gptkb:sl(2,ℝ)
|
| gptkbp:realForm |
gptkb:PSL(2,ℂ)
|
| gptkbp:universalCover |
universal covering group of PSL(2,ℝ)
|
| gptkbp:usedIn |
gptkb:hyperbolic_geometry
gptkb:Teichmüller_theory gptkb:Riemann_surfaces modular forms representation theory automorphic forms |
| gptkbp:bfsParent |
gptkb:PSL(2,ℤ)
gptkb:SL(2,ℝ) |
| gptkbp:bfsLayer |
6
|