Projective Special Linear Group of 2x2 Real Matrices

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people gptkb:Lie_group
gptkbp:actsOn	gptkb:hyperbolic_plane
gptkbp:alsoKnownAs	gptkb:PSL(2,_R)
gptkbp:centerOfSL2R	{±I}
gptkbp:compact	true
gptkbp:definedIn	SL(2, R) modulo its center
gptkbp:dimensions	3
gptkbp:field	real numbers
gptkbp:fundamentalGroup	infinite cyclic group
gptkbp:hasConnection	true
gptkbp:hasSubgroup	gptkb:modular_group_PSL(2,_Z)
https://www.w3.org/2000/01/rdf-schema#label	Projective Special Linear Group of 2x2 Real Matrices
gptkbp:isNonAbelian	true
gptkbp:isomorphicTo	orientation-preserving isometries of the hyperbolic plane
gptkbp:isQuotientOf	modular group
gptkbp:isSimple	true
gptkbp:Lie_algebra	gptkb:sl(2,_R)
gptkbp:orderOfElement	infinite
gptkbp:realForm	gptkb:PSL(2,_C)
gptkbp:relatedTo	gptkb:SL(2,_R) gptkb:PSL(2,_C) gptkb:PSL(2,_Z) modular group
gptkbp:universalCover	universal covering group of PSL(2, R)
gptkbp:usedIn	gptkb:geometry gptkb:hyperbolic_geometry differential geometry number theory representation theory
gptkbp:bfsParent	gptkb:PSL(2,_R)
gptkbp:bfsLayer	7