Special Linear Group of degree n over the integers

URI: https://gptkb.org/entity/Special_Linear_Group_of_degree_n_over_the_integers
GPTKB entity
Statements (46)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
gptkbp:abbreviation SL(n, Z)
gptkbp:actsOn n-dimensional integer lattice
gptkbp:application gptkb:Algebraic_K-theory
gptkb:geometry
gptkb:Number_theory
gptkb:Topology
gptkbp:centralTo {I, -I} for n even
{I} for n odd
gptkbp:compact true
gptkbp:containsElement n x n integer matrices with determinant 1
gptkbp:definedIn Group of n x n integer matrices with determinant 1
gptkbp:determinant 1
gptkbp:generation Elementary matrices
gptkbp:hasCongruenceSubgroups true
gptkbp:hasKazhdanPropertyT true (for n>2)
gptkbp:hasPropertyT true (for n>2)
gptkbp:hasSubgroup Elementary matrices
General Linear Group of degree n over the integers
https://www.w3.org/2000/01/rdf-schema#label Special Linear Group of degree n over the integers
gptkbp:identityElement Identity matrix
Matrix inverse
gptkbp:isAlgebraicGroup true
gptkbp:isCountable true
gptkbp:isDiscrete true
gptkbp:isDiscreteSubgroupOf gptkb:SL(n,_R)
gptkbp:isFinite true
gptkbp:isFinitelyGenerated true
gptkbp:isLatticeIn gptkb:SL(n,_R)
gptkbp:isMatrixGroup true
gptkbp:isNonAbelian true (for n > 2)
gptkbp:isNotNilpotent true (for n>1)
gptkbp:isNotSolvable true (for n>1)
gptkbp:isPerfect true (for n>2)
gptkbp:isResiduallyFinite true
gptkbp:isSimple false (for n=2)
true (for n>2, modulo center)
gptkbp:isTorsionFree false
gptkbp:isUnimodular true
gptkbp:isZariskiDenseIn gptkb:SL(n,_R)
gptkbp:notation SL(n, Z)
gptkbp:operator Matrix multiplication
gptkbp:relatedTo gptkb:Projective_Special_Linear_Group
Modular group (for n=2)
gptkbp:bfsParent gptkb:SL(n,Z)
gptkbp:bfsLayer 6