Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:actsOn |
upper half-plane
fractional linear transformations |
| gptkbp:alsoKnownAs |
gptkb:PSL(2,_Z)
|
| gptkbp:fixedPoints |
i and exp(2πi/3)
|
| gptkbp:form |
2x2 matrices with integer entries and determinant 1, modulo ±I
|
| gptkbp:fundamentalDomain |
region in upper half-plane bounded by |z|=1 and -1/2 < Re(z) < 1/2
|
| gptkbp:generation |
S and T
|
| gptkbp:hasSubgroup |
gptkb:SL(2,_Z)
|
| https://www.w3.org/2000/01/rdf-schema#label |
modular group (for n=2)
|
| gptkbp:importantFor |
complex analysis
modular forms number theory |
| gptkbp:isQuotientOf |
SL(2, Z) by {±I}
|
| gptkbp:loveInterest |
(ST)^3 = 1
S^2 = 1 |
| gptkbp:order |
infinite
|
| gptkbp:presentedBy |
⟨S, T | S^2 = 1, (ST)^3 = 1⟩
|
| gptkbp:S |
matrix [[0, -1], [1, 0]]
|
| gptkbp:TDP |
matrix [[1, 1], [0, 1]]
|
| gptkbp:type |
modular group
|
| gptkbp:bfsParent |
gptkb:GL(n,Z)
gptkb:SL(n,Z) |
| gptkbp:bfsLayer |
6
|