Projective Special Linear Group PSL(2, R)

URI: https://gptkb.org/entity/Projective_Special_Linear_Group_PSL(2,_R)
GPTKB entity
Statements (33)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
gptkb:Lie_group
gptkbp:actsOn upper half-plane
real projective line
gptkbp:centerOfSL(2,_R) {±I}
gptkbp:compact true
gptkbp:definedIn real numbers
gptkbp:dimensions 3
gptkbp:fundamentalGroup infinite cyclic group
gptkbp:hasApplication gptkb:hyperbolic_geometry
differential geometry
modular forms
number theory
automorphic forms
theory of Fuchsian groups
gptkbp:hasConnection true
gptkbp:hasSubgroup gptkb:PGL(2,_R)
https://www.w3.org/2000/01/rdf-schema#label Projective Special Linear Group PSL(2, R)
gptkbp:isNonAbelian true
gptkbp:isNotCompact true
gptkbp:isomorphicTo orientation-preserving isometries of hyperbolic plane
gptkbp:isQuotientOf gptkb:SL(2,_R)
center of SL(2, R)
gptkbp:isSimple true
gptkbp:isTopologically homeomorphic to open solid torus
gptkbp:Lie_algebra gptkb:sl(2,_R)
gptkbp:order infinite
gptkbp:realForm gptkb:PSL(2,_C)
gptkbp:universalCover universal covering group of PSL(2, R)
gptkbp:usedIn gptkb:Teichmüller_theory
representation theory
gptkbp:bfsParent gptkb:Special_Linear_Group_of_2x2_Real_Matrices
gptkbp:bfsLayer 8