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gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
projective line over F
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|
gptkbp:automorphismGroup
|
PGL(2, F)
|
|
gptkbp:centralTo
|
{λI | λ^2 = 1, λ in F*}
|
|
gptkbp:defines
|
group of 2x2 matrices with determinant 1 over field F
|
|
gptkbp:determinant
|
1
|
|
gptkbp:dimensions
|
3
|
|
gptkbp:field
|
F
|
|
gptkbp:fullName
|
Special Linear Group of 2x2 matrices over F
|
|
gptkbp:generation
|
elementary matrices
|
|
gptkbp:hasConnection
|
true
|
|
gptkbp:hasInnerAutomorphism
|
true
|
|
gptkbp:hasOuterAutomorphism
|
true
|
|
gptkbp:hasSubgroup
|
gptkb:Cartan_subgroup
gptkb:GL(2,_F)
dihedral group
Borel subgroup
unipotent subgroup
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(2, F)
|
|
gptkbp:isAlgebraicGroup
|
true
|
|
gptkbp:isChevalleyGroup
|
true
|
|
gptkbp:isClassicalGroup
|
true
|
|
gptkbp:isConnectedGroup
|
true if F is algebraically closed
|
|
gptkbp:isFinitelyGenerated
|
true
|
|
gptkbp:isMatrixGroup
|
true
true if F = R or C
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isNonNilpotent
|
true
|
|
gptkbp:isPerfect
|
true
|
|
gptkbp:isQuotientOf
|
gptkb:PSL(2,_F)
PSL(2, F) = SL(2, F)/center
|
|
gptkbp:isReductive
|
true
|
|
gptkbp:isSimple
|
true if |F| > 3
|
|
gptkbp:isSolvable
|
true
|
|
gptkbp:isSpecialGroup
|
true
|
|
gptkbp:isSplitGroup
|
true if F is a field
|
|
gptkbp:isUniversalCover
|
true for PSL(2, F)
|
|
gptkbp:matrixSize
|
2x2
|
|
gptkbp:notation
|
SL_2(F)
|
|
gptkbp:order
|
(q^3 - q) if F is finite field of order q
|
|
gptkbp:perfect
|
true
|
|
gptkbp:relatedTo
|
gptkb:PSL(2,_F)
|
|
gptkbp:usedIn
|
gptkb:algebraic_geometry
gptkb:Galois_theory
modular forms
number theory
quantum mechanics
representation theory
theory of modular curves
|
|
gptkbp:bfsParent
|
gptkb:Special_linear_group
|
|
gptkbp:bfsLayer
|
5
|