Special Linear Group of 2x2 Complex Matrices

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:algebraic_geometry gptkb:group_of_people gptkb:Lie_group
gptkbp:alsoKnownAs	gptkb:SL(2,_C)
gptkbp:centralTo	{±I}
gptkbp:connects	yes
gptkbp:defines	group of 2x2 complex matrices with determinant 1
gptkbp:determinant	1
gptkbp:dimensions	3
gptkbp:field	complex numbers
gptkbp:hasSubgroup	General Linear Group of 2x2 Complex Matrices Special Linear Group of 2x2 Real Matrices SL(2, R) Special Unitary Group SU(2)
https://www.w3.org/2000/01/rdf-schema#label	Special Linear Group of 2x2 Complex Matrices
gptkbp:identityElement	2x2 identity matrix
gptkbp:isSimple	yes
gptkbp:Lie_algebra	gptkb:sl(2,_C)
gptkbp:non-compact	yes
gptkbp:notation	gptkb:SL(2,_C)
gptkbp:order	infinite
gptkbp:relatedGroup	matrix multiplication
gptkbp:relatedTo	gptkb:Lorentz_group gptkb:SU(2) gptkb:PSL(2,_C) modular group
gptkbp:topology	Kähler manifold
gptkbp:universalCover	projective special linear group PSL(2, C)
gptkbp:usedIn	gptkb:geometry gptkb:theoretical_physics number theory representation theory
gptkbp:bfsParent	gptkb:SL(2,C) gptkb:SL(2,ℂ)
gptkbp:bfsLayer	7