Projective linear group PGL(2, ℂ)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people gptkb:Lie_group gptkb:projective_linear_group
gptkbp:actsOn	gptkb:Riemann_sphere complex projective line
gptkbp:appearsIn	gptkb:algebraic_geometry gptkb:geometry complex analysis group theory
gptkbp:automorphismGroup	gptkb:Riemann_sphere complex projective line
gptkbp:centralTo	trivial group
gptkbp:compact	true
gptkbp:definedIn	complex numbers
gptkbp:dimensions	3
gptkbp:hasComplexDimension	3
gptkbp:hasConnection	false true
gptkbp:hasSubgroup	gptkb:PSL(2,_ℂ) Borel subgroup diagonal matrices modulo scalars upper triangular matrices modulo scalars
gptkbp:isAlgebraicGroup	true
gptkbp:isHomogeneousSpaceFor	itself
gptkbp:isMatrixGroup	true
gptkbp:isNonAbelian	true
gptkbp:isomorphicTo	gptkb:PSL(2,_ℂ)
gptkbp:isProjectiveGroup	true
gptkbp:isQuotientOf	gptkb:GL(2,_ℂ) center of GL(2, ℂ)
gptkbp:isReductive	true
gptkbp:isSimple	true
gptkbp:Lie_algebra	gptkb:sl(2,_ℂ)
gptkbp:notation	gptkb:PGL(2,_ℂ) gptkb:PGL_2(ℂ)
gptkbp:order	infinite
gptkbp:realForm	gptkb:PGL(2,_ℝ)
gptkbp:relatedGroup	projective transformations of the complex projective line
gptkbp:relatedTo	gptkb:Möbius_transformations
gptkbp:universalCover	none
gptkbp:usedIn	gptkb:conformal_geometry gptkb:hyperbolic_geometry moduli theory Kleinian groups
gptkbp:bfsParent	gptkb:Möbius_transformation
gptkbp:bfsLayer	7
https://www.w3.org/2000/01/rdf-schema#label	Projective linear group PGL(2, ℂ)