|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:centerOrder
|
2
|
|
gptkbp:centralTo
|
{I, -I}
|
|
gptkbp:connects
|
true
|
|
gptkbp:defines
|
Group of 3x3 real matrices with determinant 1
|
|
gptkbp:dimensions
|
8
|
|
gptkbp:field
|
real numbers
|
|
gptkbp:fullName
|
Special Linear Group of degree 3 over the real numbers
|
|
gptkbp:fundamentalGroup
|
Z
|
|
gptkbp:generation
|
elementary matrices
|
|
gptkbp:hasCartanSubalgebra
|
diagonal traceless matrices
|
|
gptkbp:hasMaximalTorus
|
diagonal matrices with determinant 1
|
|
gptkbp:hasSubgroup
|
gptkb:SL(2,_R)
gptkb:SO(3)
GL(3, R)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(3, R)
|
|
gptkbp:isConnectedGroup
|
true
|
|
gptkbp:isNonCompactGroup
|
true
|
|
gptkbp:isQuotientOf
|
PSL(3, R)
|
|
gptkbp:isReductive
|
true
|
|
gptkbp:isSemisimple
|
true
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:Lie_algebra
|
sl(3, R)
|
|
gptkbp:maximalCompactSubgroup
|
gptkb:SO(3)
|
|
gptkbp:non-compact
|
true
|
|
gptkbp:notation
|
SL(3, ℝ)
|
|
gptkbp:order
|
infinite
|
|
gptkbp:rank
|
2
|
|
gptkbp:realForm
|
true
SL(3, C)
|
|
gptkbp:relatedGroup
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:relatedTo
|
gptkb:SL(2,_R)
gptkb:SL(n,_R)
GL(3, R)
PSL(3, R)
|
|
gptkbp:structure
|
non-abelian
|
|
gptkbp:topology
|
real manifold
|
|
gptkbp:type
|
gptkb:A2
|
|
gptkbp:universalCover
|
simply connected Lie group covering SL(3, R)
|
|
gptkbp:usedIn
|
differential geometry
number theory
physics
representation theory
|
|
gptkbp:Weyl_group
|
S3
|
|
gptkbp:bfsParent
|
gptkb:SL(3,_Z)
|
|
gptkbp:bfsLayer
|
7
|