|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
real n-dimensional vector space
|
|
gptkbp:centralTo
|
{I_n} if n is odd, {I_n, -I_n} if n is even
|
|
gptkbp:connects
|
true
|
|
gptkbp:definedIn
|
the group of n x n real matrices with determinant 1
|
|
gptkbp:dimensions
|
n^2 - 1
|
|
gptkbp:fullName
|
Special Linear Group of degree n over the real numbers
|
|
gptkbp:hasFiniteCenter
|
true
|
|
gptkbp:hasSubgroup
|
gptkb:GL(n,_R)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(n, R)
|
|
gptkbp:identityElement
|
identity matrix
matrix inverse
|
|
gptkbp:isAlgebraicGroup
|
true
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isSimple
|
true for n > 2
|
|
gptkbp:isSimpleConnected
|
false for n > 2
|
|
gptkbp:Lie_algebra
|
gptkb:sl(n,_R)
|
|
gptkbp:maximalCompactSubgroup
|
gptkb:SO(n)
|
|
gptkbp:noncompact
|
true
|
|
gptkbp:notation
|
SL_n(R)
|
|
gptkbp:realForm
|
gptkb:SL(n,_C)
|
|
gptkbp:relatedGroup
|
matrix multiplication
|
|
gptkbp:universalCover
|
universal covering group of SL(n, R)
|
|
gptkbp:usedIn
|
gptkb:algebraic_geometry
differential geometry
number theory
physics
representation theory
|
|
gptkbp:bfsParent
|
gptkb:SO(n)
gptkb:special_linear_group_SL(n,_R)
|
|
gptkbp:bfsLayer
|
6
|