|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
R^2
|
|
gptkbp:centralTo
|
scalar multiples of identity matrix
|
|
gptkbp:complexification
|
gptkb:GL(2,C)
|
|
gptkbp:component
|
gptkb:Z/2Z
|
|
gptkbp:containsElement
|
invertible 2x2 real matrices
|
|
gptkbp:determinant
|
GL(2,R) → R\\{0}
nonzero real number
|
|
gptkbp:dimensions
|
4
|
|
gptkbp:field
|
real numbers
|
|
gptkbp:fullName
|
gptkb:General_Linear_Group_of_2x2_real_matrices
|
|
gptkbp:hasConnection
|
false
|
|
gptkbp:hasSubgroup
|
gptkb:SO(2)
gptkb:SL(2,R)
gptkb:O(2)
|
|
gptkbp:hasTopology
|
standard topology from R^4
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
GL(2,R)
|
|
gptkbp:identityElement
|
2x2 identity matrix
|
|
gptkbp:isAlgebraicGroup
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isQuotientOf
|
gptkb:GL(2,R)/SL(2,R)
|
|
gptkbp:isReductive
|
true
|
|
gptkbp:isSimple
|
false
|
|
gptkbp:Lie_algebra
|
gl(2,R)
|
|
gptkbp:maximalCompactSubgroup
|
gptkb:O(2)
|
|
gptkbp:numberOfConnectedComponents
|
2
|
|
gptkbp:order
|
infinite
|
|
gptkbp:realRank
|
2
|
|
gptkbp:relatedGroup
|
matrix multiplication
|
|
gptkbp:relatedTo
|
linear transformations of R^2
|
|
gptkbp:representationTheory
|
well-studied
|
|
gptkbp:usedIn
|
gptkb:algebraic_geometry
differential geometry
number theory
physics
representation theory
|
|
gptkbp:bfsParent
|
gptkb:PSL(2,R)
gptkb:SL(2,R)_symmetry
|
|
gptkbp:bfsLayer
|
7
|