Special Linear Group of 2x2 integer matrices with determinant 1
GPTKB entity
Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:actsOn |
upper half-plane
|
| gptkbp:alsoKnownAs |
gptkb:SL(2,_Z)
|
| gptkbp:centralTo |
{I, -I}
|
| gptkbp:containsElement |
2x2 integer matrices with determinant 1
|
| gptkbp:finitelyGenerated |
true
|
| gptkbp:generation |
S = [[0, -1], [1, 0]]
T = [[1, 1], [0, 1]] |
| gptkbp:hasSubgroup |
GL(2, Z)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Special Linear Group of 2x2 integer matrices with determinant 1
|
| gptkbp:identityElement |
2x2 identity matrix
|
| gptkbp:importantFor |
gptkb:hyperbolic_geometry
modular forms number theory modular group theory |
| gptkbp:isQuotientOf |
gptkb:PSL(2,_Z)
|
| gptkbp:notation |
gptkb:SL(2,_Z)
|
| gptkbp:operator |
matrix multiplication
|
| gptkbp:order |
infinite
|
| gptkbp:presentedBy |
<S, T | S^4 = I, (ST)^3 = I>
|
| gptkbp:relatedGroup |
gptkb:group_of_people
orthogonal group |
| gptkbp:bfsParent |
gptkb:SL(2,_Z)
|
| gptkbp:bfsLayer |
6
|