|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
C^n
|
|
gptkbp:algebraicGroup
|
true
|
|
gptkbp:application
|
gptkb:algebraic_geometry
differential geometry
physics
quantum mechanics
representation theory
|
|
gptkbp:centralTo
|
scalar matrices with nonzero complex entries
|
|
gptkbp:connects
|
true
|
|
gptkbp:definedIn
|
the group of n x n invertible matrices with complex entries
|
|
gptkbp:dimensions
|
n^2
|
|
gptkbp:field
|
complex numbers
|
|
gptkbp:fullName
|
general linear group of degree n over the complex numbers
|
|
gptkbp:hasSubgroup
|
gptkb:SL(n,_C)
gptkb:GL(n,_C^n)
|
|
gptkbp:homotopyType
|
homotopy equivalent to U(n)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
GL(n, C)
|
|
gptkbp:identityElement
|
identity matrix
matrix inverse
|
|
gptkbp:isSimple
|
false
|
|
gptkbp:noncompact
|
true
|
|
gptkbp:notation
|
gptkb:GL(n,_C)
|
|
gptkbp:operator
|
matrix multiplication
|
|
gptkbp:reductive
|
true
|
|
gptkbp:relatedTo
|
gptkb:SL(n,_C)
gptkb:unitary_group_U(n)
gptkb:GL(n,_R)
gptkb:orthogonal_group_O(n,_C)
|
|
gptkbp:topology
|
complex Lie group topology
|
|
gptkbp:bfsParent
|
gptkb:复李群
gptkb:Hopf_manifold
|
|
gptkbp:bfsLayer
|
6
|