|
gptkbp:instanceOf
|
gptkb:group_of_people
|
|
gptkbp:abbreviation
|
gptkb:GL(n,_F)
|
|
gptkbp:actsOn
|
gptkb:Vector
|
|
gptkbp:compact
|
true
|
|
gptkbp:contains
|
orthogonal group
|
|
gptkbp:defines
|
group of invertible n×n matrices over a field F
|
|
gptkbp:dimensions
|
n^2
|
|
gptkbp:field
|
F
abstract algebra
|
|
gptkbp:hasSubgroup
|
orthogonal group
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
general linear group
|
|
gptkbp:identityElement
|
identity matrix
|
|
gptkbp:isAlgebraicGroup
|
true
|
|
gptkbp:isChevalleyGroup
|
true
|
|
gptkbp:isClassicalGroup
|
true
|
|
gptkbp:isConnectedGroup
|
true
|
|
gptkbp:isDefinedOver
|
any field F
|
|
gptkbp:isFinite
|
if F is finite
if F is infinite
|
|
gptkbp:isFundamentalIn
|
gptkb:algebraic_geometry
differential geometry
group theory
representation theory
|
|
gptkbp:isGroupOfAutomorphisms
|
true
|
|
gptkbp:isGroupScheme
|
true
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isNonNilpotent
|
true
|
|
gptkbp:isQuotientOf
|
projective general linear group
|
|
gptkbp:isReductive
|
true
|
|
gptkbp:isSimple
|
false
|
|
gptkbp:isSolvable
|
true
|
|
gptkbp:isTopologicalGroup
|
true
|
|
gptkbp:isZariskiDense
|
true
|
|
gptkbp:notation
|
gptkb:GL(n,_F)
|
|
gptkbp:operator
|
matrix multiplication
|
|
gptkbp:order
|
(q^n-1)(q^n-q)...(q^n-q^{n-1}) for GL(n, F_q)
|
|
gptkbp:relatedTo
|
orthogonal group
projective linear group
|
|
gptkbp:represents
|
invertible matrices
|
|
gptkbp:bfsParent
|
gptkb:group_of_people
|
|
gptkbp:bfsLayer
|
4
|