Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:actsOn |
gptkb:geometry
real projective line |
| gptkbp:application |
gptkb:geometry
gptkb:hyperbolic_geometry automorphisms of projective line |
| gptkbp:centralTo |
trivial
|
| 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:hasSubgroup |
gptkb:PSL(2,ℝ)
Borel subgroup SO(2,ℝ) |
| https://www.w3.org/2000/01/rdf-schema#label |
PGL(2,ℝ)
|
| gptkbp:isomorphicTo |
PSL(2,ℝ) × C2
|
| gptkbp:isQuotientOf |
GL(2,ℝ)
center of GL(2,ℝ) |
| gptkbp:Lie_algebra |
gptkb:sl(2,ℝ)
|
| gptkbp:notation |
gptkb:PGL(2,R)
PGL_2(ℝ) |
| gptkbp:order |
infinite
|
| gptkbp:originatedIn |
projective transformations
|
| gptkbp:relatedTo |
gptkb:Möbius_transformations
gptkb:PSL(2,ℝ) fractional linear transformations |
| gptkbp:structure |
connected
non-compact simple (modulo center) |
| gptkbp:bfsParent |
gptkb:projective_line_over_ℝ
|
| gptkbp:bfsLayer |
7
|