|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:centralTo
|
set of scalar matrices zI with z^n=1
|
|
gptkbp:compact
|
true
|
|
gptkbp:complexification
|
gptkb:SL(n,R)
|
|
gptkbp:definedIn
|
the group of n x n complex matrices with determinant 1
|
|
gptkbp:dimensions
|
n^2 - 1
|
|
gptkbp:field
|
C
|
|
gptkbp:fullName
|
gptkb:Special_Linear_Group_of_degree_n_over_the_complex_numbers
|
|
gptkbp:hasConnection
|
true
|
|
gptkbp:hasSubgroup
|
gptkb:GL(n,C)
|
|
gptkbp:hasTrivialCenter
|
false
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(n,C)
|
|
gptkbp:identityElement
|
identity matrix
|
|
gptkbp:isAlgebraicGroup
|
C
true
|
|
gptkbp:isClassicalGroup
|
true
|
|
gptkbp:isConnectedFor
|
n > 0
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isNonCompactFor
|
n > 1
|
|
gptkbp:isPerfect
|
true
|
|
gptkbp:isQuotientOf
|
PSL(n,C)
|
|
gptkbp:isReductive
|
true
|
|
gptkbp:isReductiveFor
|
n > 1
|
|
gptkbp:isSemisimple
|
true
|
|
gptkbp:isSemisimpleFor
|
n > 1
|
|
gptkbp:isSimple
|
true
n > 1
|
|
gptkbp:Lie_algebra
|
gptkb:sl(n,C)
|
|
gptkbp:notation
|
gptkb:SL(n,C)
|
|
gptkbp:realForm
|
gptkb:SL(n,C)
|
|
gptkbp:relatedGroup
|
matrix multiplication
|
|
gptkbp:relatedTo
|
gptkb:GL(n,C)
|
|
gptkbp:universalCover
|
itself (simply connected)
|
|
gptkbp:usedIn
|
gptkb:algebraic_geometry
gptkb:theoretical_physics
differential geometry
representation theory
|
|
gptkbp:bfsParent
|
gptkb:GL(n,C)
gptkb:special_linear_group_SL(n,C)
gptkb:special_linear_group_SL(n,R)
|
|
gptkbp:bfsLayer
|
7
|