SL 2(R) (in analytic topology)

GPTKB entity

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
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	8
https://www.w3.org/2000/01/rdf-schema#label	SL 2(R) (in analytic topology)