Statements (42)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
modular group discrete group |
| gptkbp:action |
fractional linear transformation
|
| gptkbp:actsOn |
upper half-plane
|
| gptkbp:application |
gptkb:algebraic_geometry
gptkb:string_theory number theory theory of modular forms theory of Riemann surfaces topology of surfaces monodromy of differential equations |
| gptkbp:centralTo |
{±I}
|
| gptkbp:containsElement |
2x2 integer matrices with determinant 1
|
| gptkbp:definedIn |
integers
|
| gptkbp:generation |
S = [[0,-1],[1,0]]
T = [[1,1],[0,1]] |
| gptkbp:hasProperty |
modular group
non-abelian orthogonal group finitely generated not finite free product of cyclic groups of order 4 and 6 modulo center lattice in SL(2,R) |
| gptkbp:hasSubgroup |
gptkb:SL(2,R)
|
| https://www.w3.org/2000/01/rdf-schema#label |
modular group SL(2,Z)
|
| gptkbp:isQuotientOf |
gptkb:PSL(2,Z)
|
| gptkbp:loveInterest |
(ST)^3 = I
S^4 = I |
| gptkbp:namedAfter |
modular transformations
|
| gptkbp:notation |
gptkb:SL(2,Z)
|
| gptkbp:operator |
matrix multiplication
|
| gptkbp:order |
infinite
|
| gptkbp:presentedBy |
<S,T | S^4 = I, (ST)^3 = I>
|
| gptkbp:relatedTo |
gptkb:monodromy_group
gptkb:modular_curves modular forms automorphic forms elliptic curves congruence subgroups |
| gptkbp:bfsParent |
gptkb:modular_function_j(z)
|
| gptkbp:bfsLayer |
6
|