Statements (50)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:actsOn |
gptkb:integer_lattice_Z^n
|
| gptkbp:application |
gptkb:geometry
gptkb:topology gptkb:algebraic_K-theory gptkb:hyperbolic_geometry gptkb:modular_curves gptkb:Teichmüller_theory gptkb:monodromy_groups coding theory cryptography crystallography dynamical systems modular forms number theory representation theory algebraic groups lattice theory automorphic forms symplectic geometry group cohomology arithmetic groups automorphic representations mapping class groups modular symbols lattice reduction algorithms |
| gptkbp:centralTo |
{I, -I} for n even, {I} for n odd
|
| gptkbp:definedIn |
the group of n×n integer matrices with determinant 1
|
| gptkbp:fullName |
gptkb:Special_Linear_Group_of_degree_n_over_the_integers
|
| gptkbp:generation |
elementary matrices
|
| gptkbp:hasSubgroup |
gptkb:GL(n,Z)
|
| https://www.w3.org/2000/01/rdf-schema#label |
SL(n,Z)
|
| gptkbp:identityElement |
identity matrix
matrix inverse |
| gptkbp:isQuotientOf |
gptkb:PSL(n,Z)
|
| gptkbp:notableGroup |
gptkb:SL(3,Z)
gptkb:SL(2,Z) |
| gptkbp:notation |
gptkb:SL(n,ℤ)
|
| gptkbp:operator |
matrix multiplication
|
| gptkbp:order |
infinite (for n ≥ 2)
|
| gptkbp:property |
modular group
orthogonal group finitely generated discrete subgroup of SL(n,R) non-abelian for n ≥ 2 |
| gptkbp:relatedTo |
gptkb:modular_group_(for_n=2)
congruence subgroups automorphism group of free abelian group of rank n |
| gptkbp:bfsParent |
gptkb:modular_group
|
| gptkbp:bfsLayer |
5
|