|
gptkbp:instanceOf
|
gptkb:group_of_people
discrete group
|
|
gptkbp:actsOn
|
upper half-plane
|
|
gptkbp:centralTo
|
{I, -I}
|
|
gptkbp:contains
|
modular group
|
|
gptkbp:containsElement
|
2x2 integer matrices with determinant 1
|
|
gptkbp:determinant
|
1
|
|
gptkbp:field
|
integers
|
|
gptkbp:fullName
|
gptkb:Special_Linear_Group_of_2x2_integer_matrices_with_determinant_1
|
|
gptkbp:generation
|
matrices S and T
|
|
gptkbp:hasSubgroup
|
gptkb:principal_congruence_subgroup
gptkb:SL(2,_ℝ)
congruence subgroups
|
|
gptkbp:heldBy
|
modular group
non-abelian group
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(2, ℤ)
|
|
gptkbp:indexInGL(2,_ℤ)
|
2
|
|
gptkbp:isQuotientOf
|
PSL(2, ℤ)
|
|
gptkbp:notation
|
gptkb:SL(2,_Z)
|
|
gptkbp:order
|
infinite
|
|
gptkbp:presentedBy
|
<S, T | S^4 = I, (ST)^3 = I>
|
|
gptkbp:rank
|
2
|
|
gptkbp:relatedTo
|
gptkb:modular_curves
gptkb:Farey_tessellation
Hecke operators
modular forms
modular group
continued fractions
modular group action
modular symbols
modular group generators
modular group relations
modular group fundamental domain
modular group cosets
modular group presentations
modular group subgroups
|
|
gptkbp:S
|
[[0, -1], [1, 0]]
|
|
gptkbp:TDP
|
[[1, 1], [0, 1]]
|
|
gptkbp:usedIn
|
gptkb:algebraic_geometry
gptkb:topology
gptkb:hyperbolic_geometry
modular forms
number theory
theory of automorphic forms
|
|
gptkbp:bfsParent
|
gptkb:SL(2,_Z)
|
|
gptkbp:bfsLayer
|
6
|