|
gptkbp:instanceOf
|
gptkb:algebraic_geometry
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
ℂ^n
|
|
gptkbp:centralTo
|
set of scalar matrices λI with λ^n = 1
|
|
gptkbp:compact
|
true
|
|
gptkbp:complexification
|
gptkb:SL(n,_ℝ)
|
|
gptkbp:definedIn
|
the group of n×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:hasMaximalSubgroup
|
gptkb:SU(n)
|
|
gptkbp:hasSubgroup
|
GL(n, ℂ)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(n, ℂ)
|
|
gptkbp:isAlgebraicGroup
|
true
ℂ
|
|
gptkbp:isChevalleyGroup
|
true
|
|
gptkbp:isClassicalGroup
|
true
|
|
gptkbp:isComplexLieGroup
|
true
|
|
gptkbp:isConnectedAlgebraicGroup
|
true
|
|
gptkbp:isLinearLieGroup
|
true
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isMatrixLieGroup
|
true
|
|
gptkbp:isPerfect
|
true
|
|
gptkbp:isQuotientOf
|
PSL(n, ℂ)
|
|
gptkbp:isReductive
|
true
|
|
gptkbp:isReductiveLieGroup
|
true
|
|
gptkbp:isSemisimple
|
true
|
|
gptkbp:isSemisimpleLieGroup
|
true
|
|
gptkbp:isSimple
|
true
true for n ≥ 2
|
|
gptkbp:isSimpleAlgebraicGroup
|
true
|
|
gptkbp:isSpecialGroup
|
true
|
|
gptkbp:isUnimodular
|
true
|
|
gptkbp:Lie_algebra
|
sl(n, ℂ)
|
|
gptkbp:notation
|
SL_n(ℂ)
|
|
gptkbp:relatedGroup
|
non-abelian
|
|
gptkbp:type
|
A_{n-1}
|
|
gptkbp:universalCover
|
PSL(n, ℂ)
|
|
gptkbp:usedIn
|
gptkb:algebraic_geometry
gptkb:theoretical_physics
differential geometry
representation theory
|
|
gptkbp:bfsParent
|
gptkb:orthogonal_group
|
|
gptkbp:bfsLayer
|
5
|