|
gptkbp:instanceOf
|
gptkb:group_of_people
|
|
gptkbp:actsOn
|
complex projective line
|
|
gptkbp:automorphismGroup
|
itself
|
|
gptkbp:centralTo
|
trivial group
|
|
gptkbp:compact
|
true
|
|
gptkbp:contains
|
gptkb:PSL(2,C)
finite subgroups corresponding to polyhedral groups
|
|
gptkbp:dimensions
|
3
|
|
gptkbp:field
|
complex numbers
|
|
gptkbp:fullName
|
projective general linear group of 2x2 matrices over the complex numbers
|
|
gptkbp:hasConnection
|
true
|
|
gptkbp:hasSubgroup
|
diagonal matrices modulo center
unipotent matrices modulo center
Borel subgroup (upper triangular matrices modulo center)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
PGL(2,C)
|
|
gptkbp:isAlgebraicGroup
|
C
true
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isomorphicTo
|
gptkb:PSL(2,C)
|
|
gptkbp:isProjectiveGroup
|
true
|
|
gptkbp:isQuotientOf
|
gptkb:GL(2,C)
SL(2,C) by {±I}
center of GL(2,C)
|
|
gptkbp:isReductive
|
true
|
|
gptkbp:isSemisimple
|
true
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:order
|
infinite
|
|
gptkbp:relatedTo
|
gptkb:Möbius_transformations
automorphisms of the Riemann sphere
|
|
gptkbp:usedIn
|
gptkb:algebraic_geometry
gptkb:conformal_geometry
gptkb:hyperbolic_geometry
complex analysis
moduli spaces
Kleinian groups
theory of Riemann surfaces
|
|
gptkbp:bfsParent
|
gptkb:CP^1
|
|
gptkbp:bfsLayer
|
7
|