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gptkbp:instanceOf
|
gptkb:group_of_people
|
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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
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|
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)
|
|
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
|
gptkb:orthogonal_group
gptkb:modular_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:SL(n,ℤ)
|
|
gptkbp:bfsLayer
|
10
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SL(n,Z)
|