Projective linear group PGL(2, C)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people gptkb:Lie_group
gptkbp:actsOn	gptkb:Riemann_sphere complex projective line
gptkbp:automorphismGroup	gptkb:Riemann_sphere complex projective line
gptkbp:centralTo	trivial group
gptkbp:compact	true
gptkbp:dimensions	3
gptkbp:hasConnection	true
gptkbp:hasSubgroup	gptkb:PGL(2,_R) gptkb:PSL(2,_C) gptkb:PSL(2,_R) modular group Borel subgroup diagonal matrices modulo scalars upper triangular matrices modulo scalars
https://www.w3.org/2000/01/rdf-schema#label	Projective linear group PGL(2, C)
gptkbp:isAlgebraicGroup	true
gptkbp:isDefinedOver	complex numbers
gptkbp:isHomogeneousSpaceFor	itself
gptkbp:isMatrixGroup	true
gptkbp:isNonAbelian	true
gptkbp:isomorphicTo	gptkb:PSL(2,_C)
gptkbp:isProjectiveGroup	true
gptkbp:isQuotientOf	gptkb:C* gptkb:GL(2,_C) SL(2, C) by {±I}
gptkbp:isReductive	true
gptkbp:isSimple	true
gptkbp:Lie_algebra	gptkb:sl(2,_C)
gptkbp:order	infinite
gptkbp:relatedGroup	gptkb:Möbius_transformations fractional linear transformations automorphisms of the Riemann sphere linear automorphisms of CP^1
gptkbp:relatedTo	gptkb:Kleinian_group modular group
gptkbp:universalCover	none
gptkbp:usedIn	gptkb:algebraic_geometry gptkb:geometry gptkb:Möbius_transformations complex analysis Kleinian groups
gptkbp:bfsParent	gptkb:Linear_Fractional_Transformation gptkb:Möbius_Transformation
gptkbp:bfsLayer	8