Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:actsOn |
real projective line
|
| gptkbp:compact |
true
|
| gptkbp:component |
C2 (cyclic group of order 2)
|
| gptkbp:contains |
PSL(2, ℝ)
|
| gptkbp:definedIn |
GL(2, ℝ) modulo scalar matrices
|
| gptkbp:dimensions |
3
|
| gptkbp:field |
ℝ
|
| gptkbp:fullName |
Projective General Linear Group of 2x2 real matrices
|
| gptkbp:hasConnection |
false
|
| gptkbp:hasTwoComponents |
true
|
| https://www.w3.org/2000/01/rdf-schema#label |
PGL(2, ℝ)
|
| gptkbp:isHomomorphicImageOf |
GL(2, ℝ)
|
| gptkbp:isMatrixGroup |
true
|
| gptkbp:isQuotientOf |
GL(2, ℝ)
center of GL(2, ℝ) |
| gptkbp:isSimple |
false
|
| gptkbp:isSimpleModCenter |
true
|
| gptkbp:notation |
gptkb:PGL(2,_R)
PGL_2(ℝ) |
| gptkbp:originatedIn |
gptkb:geometry
gptkb:conformal_geometry gptkb:hyperbolic_geometry |
| gptkbp:realForm |
gptkb:PGL(2,_C)
|
| gptkbp:relatedTo |
PSL(2, ℝ)
|
| gptkbp:universalCover |
gptkb:SL(2,_ℝ)
|
| gptkbp:usedIn |
differential geometry
modular forms automorphic forms |
| gptkbp:bfsParent |
gptkb:Projective_linear_group_PGL(2,_ℂ)
|
| gptkbp:bfsLayer |
7
|