|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
C^n
|
|
gptkbp:centralTo
|
scalar matrices
|
|
gptkbp:compact
|
true
|
|
gptkbp:connects
|
true
|
|
gptkbp:definedIn
|
the group of n x n invertible matrices with complex entries
|
|
gptkbp:determinant
|
gptkb:SL(n,C)
GL(n,C) → C*
|
|
gptkbp:dimensions
|
n^2
|
|
gptkbp:field
|
complex numbers
|
|
gptkbp:fullName
|
general linear group of degree n over the complex numbers
|
|
gptkbp:hasDeterminantMap
|
true
|
|
gptkbp:hasMaximalSubgroup
|
U(n)
|
|
gptkbp:hasSubgroup
|
gptkb:SL(n,C)
gptkb:GL(n,C^n)
gptkb:Sp(2n,C)
U(n)
O(n,C)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
GL(n,C)
|
|
gptkbp:identityElement
|
identity matrix
matrix inverse
|
|
gptkbp:isAlgebraicGroup
|
C
true
|
|
gptkbp:isClassicalGroup
|
true
|
|
gptkbp:isComplexLieGroup
|
true
|
|
gptkbp:isConnectedGroup
|
true
|
|
gptkbp:isGroupScheme
|
true
|
|
gptkbp:isHomogeneousSpace
|
false
|
|
gptkbp:isLinearGroupOver
|
C
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isNonCompactLieGroup
|
true
|
|
gptkbp:isQuotientOf
|
gptkb:PGL(n,C)
|
|
gptkbp:isReductive
|
true
|
|
gptkbp:isSemisimpleGroup
|
false
|
|
gptkbp:isSimple
|
false
|
|
gptkbp:notation
|
gptkb:GL(n,C)
|
|
gptkbp:operator
|
matrix multiplication
|
|
gptkbp:order
|
infinite
|
|
gptkbp:realForm
|
gptkb:GL(n,R)
|
|
gptkbp:relatedTo
|
determinant
|
|
gptkbp:topology
|
gptkb:Lie_group
|
|
gptkbp:bfsParent
|
gptkb:unitary_group_U(n)
|
|
gptkbp:bfsLayer
|
6
|