|
gptkbp:instanceOf
|
gptkb:group_of_people
|
|
gptkbp:actsOn
|
Z^n
|
|
gptkbp:application
|
gptkb:algebraic_K-theory
modular forms
lattice theory
arithmetic groups
|
|
gptkbp:centralTo
|
{I, -I} for n even, {I} for n odd
|
|
gptkbp:containsElement
|
n x n invertible integer matrices
|
|
gptkbp:definedIn
|
the group of n x n invertible matrices with integer entries
|
|
gptkbp:determinant
|
±1
|
|
gptkbp:discreteGroup
|
true
|
|
gptkbp:field
|
Z
|
|
gptkbp:finitelyGenerated
|
true
|
|
gptkbp:fullName
|
gptkb:general_linear_group_of_degree_n_over_the_integers
|
|
gptkbp:generatorsKnown
|
true
|
|
gptkbp:hasSubgroup
|
GL_n(Q)
SL_n(Z)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
GL n(Z)
|
|
gptkbp:identityElement
|
identity matrix
matrix inverse
|
|
gptkbp:isNonAbelian
|
true (for n > 1)
|
|
gptkbp:isQuotientOf
|
GL_n(Z)/SL_n(Z) ≅ {±1}
|
|
gptkbp:notation
|
gptkb:GL_n(Z)
|
|
gptkbp:operator
|
matrix multiplication
|
|
gptkbp:order
|
infinite (for n > 1)
|
|
gptkbp:parent
|
gptkb:GL_n(R)
|
|
gptkbp:relatedTo
|
automorphism group of Z^n
|
|
gptkbp:type
|
modular group
|
|
gptkbp:bfsParent
|
gptkb:GL(n,Z)
|
|
gptkbp:bfsLayer
|
6
|