|
gptkbp:instanceOf
|
gptkb:group_of_people
|
|
gptkbp:actsOn
|
gptkb:Riemann_sphere
complex projective line
extended complex plane
|
|
gptkbp:associativity
|
yes
|
|
gptkbp:closed
|
composition of transformations
|
|
gptkbp:consistsOf
|
gptkb:Möbius_transformations
|
|
gptkbp:dimensions
|
6
|
|
gptkbp:field
|
gptkb:mathematics
|
|
gptkbp:hasApplication
|
gptkb:geometry
gptkb:Teichmüller_theory
dynamical systems
mathematical physics
moduli spaces
complex function theory
|
|
gptkbp:hasElementForm
|
(az + b)/(cz + d), ad-bc ≠ 0
|
|
gptkbp:hasInverseElement
|
inverse Möbius transformation
|
|
gptkbp:hasSubgroup
|
gptkb:conformal_group
gptkb:homeomorphism_group_of_the_Riemann_sphere
gptkb:loxodromic_transformations
gptkb:rotation_group_of_the_sphere
elliptic transformations
hyperbolic transformations
parabolic transformations
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Möbius group
|
|
gptkbp:identityElement
|
identity transformation
|
|
gptkbp:isNonAbelian
|
yes
|
|
gptkbp:isomorphicTo
|
gptkb:PSL(2,_C)
|
|
gptkbp:matrixRepresentation
|
2x2 complex matrices modulo scalar multiples
|
|
gptkbp:namedAfter
|
gptkb:August_Ferdinand_Möbius
|
|
gptkbp:order
|
infinite
|
|
gptkbp:preserves
|
angles
circles
cross-ratio
|
|
gptkbp:relatedTo
|
gptkb:geometry
gptkb:hyperbolic_geometry
gptkb:Kleinian_group
complex analysis
modular group
|
|
gptkbp:represents
|
fractional linear transformations
|
|
gptkbp:type
|
gptkb:Lie_group
|
|
gptkbp:usedIn
|
gptkb:string_theory
gptkb:theory_of_automorphic_functions
mathematical physics
conformal mapping
complex dynamics
|
|
gptkbp:bfsParent
|
gptkb:Riemann_sphere
|
|
gptkbp:bfsLayer
|
6
|