SL 2(R) (in analytic topology)

URI: https://gptkb.org/entity/SL_2(R)_(in_analytic_topology)
GPTKB entity
Statements (45)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
gptkb:topology
gptkb:Lie_group
gptkbp:actsOn gptkb:projective_line_over_R
upper half-plane
gptkbp:centralTo {±I}
gptkbp:connects true
gptkbp:definedIn group of 2x2 real matrices with determinant 1
gptkbp:dimensions 3
gptkbp:field real numbers
gptkbp:fundamentalGroup Z
gptkbp:hasBorelSubgroup upper triangular matrices with determinant 1
gptkbp:hasBruhatDecomposition true
gptkbp:hasCartanSubgroup diagonal matrices with determinant 1
gptkbp:hasDiscreteSubgroup gptkb:Fuchsian_groups
modular group SL_2(Z)
gptkbp:hasIwasawaDecomposition true
gptkbp:hasSubgroup gptkb:SO(2)
diagonal matrices with determinant 1
https://www.w3.org/2000/01/rdf-schema#label SL 2(R) (in analytic topology)
gptkbp:identityElement 2x2 identity matrix
gptkbp:isDoubleCoverOf gptkb:PSL_2(R)
gptkbp:isMatrixGroup true
gptkbp:isNonAbelian true
gptkbp:isNonCompactSimpleLieGroup true
gptkbp:isQuotientOf gptkb:PSL_2(R)
gptkbp:isRealLieGroup true
gptkbp:isReductive true
gptkbp:isSemisimple true
gptkbp:isSimple true
gptkbp:Lie_algebra sl_2(R)
gptkbp:maximalCompactSubgroup gptkb:SO(2)
gptkbp:nonCompact true
gptkbp:realForm gptkb:SL_2(C)
gptkbp:relatedGroup matrix multiplication
gptkbp:simplyConnected false
gptkbp:universalCover universal covering group of SL_2(R)
gptkbp:usedIn gptkb:hyperbolic_geometry
differential geometry
modular forms
number theory
representation theory
automorphic forms
gptkbp:bfsParent gptkb:SL_2(Z)
gptkbp:bfsLayer 7