Special Linear Group of 2x2 Real Matrices

URI: https://gptkb.org/entity/Special_Linear_Group_of_2x2_Real_Matrices
GPTKB entity
Statements (29)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
gptkb:Lie_group
gptkbp:application gptkb:Representation_theory
gptkb:Quantum_mechanics
gptkb:Hyperbolic_geometry
gptkbp:centralTo {±I}
gptkbp:commonName gptkb:SL(2,_R)
gptkbp:connects Yes
gptkbp:containsElement 2x2 real matrices with determinant 1
gptkbp:definedIn Real numbers
gptkbp:determinant 1
gptkbp:dimensions 3
gptkbp:hasSubgroup gptkb:Special_Orthogonal_Group_SO(2)
Upper triangular matrices with determinant 1
https://www.w3.org/2000/01/rdf-schema#label Special Linear Group of 2x2 Real Matrices
gptkbp:identityElement 2x2 identity matrix
Matrix inverse
gptkbp:isNonAbelian Yes
gptkbp:isSimple Yes
gptkbp:non-compact Yes
gptkbp:notation gptkb:SL(2,_R)
gptkbp:order Infinite
gptkbp:relatedGroup Matrix multiplication
gptkbp:relatedTo gptkb:Lie_algebra_sl(2,_R)
gptkb:Projective_Special_Linear_Group_PSL(2,_R)
gptkbp:unimodular Yes
gptkbp:universalCover gptkb:Universal_covering_group_of_SL(2,_R)
gptkbp:bfsParent gptkb:SL_2(R)
gptkbp:bfsLayer 7