|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:centralTo
|
scalar matrices with nonzero complex entries
|
|
gptkbp:compact
|
true
|
|
gptkbp:contains
|
gptkb:SL(2,_ℂ)
|
|
gptkbp:containsElement
|
all 2×2 invertible matrices over ℂ
|
|
gptkbp:determinant
|
nonzero complex number
|
|
gptkbp:dimensions
|
4
|
|
gptkbp:field
|
ℂ
|
|
gptkbp:fullName
|
general linear group of 2×2 invertible complex matrices
|
|
gptkbp:hasConnection
|
true
|
|
gptkbp:hasSubgroup
|
gptkb:SL(2,_ℂ)
upper triangular matrices
diagonal matrices
lower triangular matrices
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
GL(2, ℂ)
|
|
gptkbp:identityElement
|
2×2 identity matrix
|
|
gptkbp:invertible
|
true
|
|
gptkbp:isAlgebraicGroup
|
true
|
|
gptkbp:isClassicalGroup
|
true
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isQuotientOf
|
gptkb:PGL(2,_ℂ)
|
|
gptkbp:isReductive
|
true
|
|
gptkbp:isSimple
|
false
|
|
gptkbp:Lie_algebra
|
gl(2, ℂ)
|
|
gptkbp:LieAlgebraDimension
|
4
|
|
gptkbp:notation
|
gptkb:GL(2,_ℂ)
GL2(C)
GL_2(ℂ)
|
|
gptkbp:operator
|
matrix multiplication
|
|
gptkbp:order
|
infinite
|
|
gptkbp:relatedTo
|
gptkb:SL(2,_ℂ)
GL(n, ℂ)
GL(2, ℝ)
|
|
gptkbp:representationTheory
|
important in mathematics and physics
|
|
gptkbp:usedIn
|
gptkb:algebraic_geometry
differential geometry
quantum mechanics
representation theory
linear algebra
|
|
gptkbp:bfsParent
|
gptkb:Projective_linear_group_PGL(2,_ℂ)
|
|
gptkbp:bfsLayer
|
7
|