special linear group of 2x2 integer matrices

URI: https://gptkb.org/entity/special_linear_group_of_2x2_integer_matrices
GPTKB entity
Statements (34)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
orthogonal group
gptkbp:abbreviation gptkb:SL(2,_Z)
gptkbp:actsOn upper half-plane
gptkbp:centralTo {I, -I}
gptkbp:containsElement 2x2 matrices with integer entries and determinant 1
gptkbp:definedIn group of 2x2 integer matrices with determinant 1
gptkbp:hasApplication gptkb:hyperbolic_geometry
modular forms
number theory
automorphic forms
gptkbp:hasCongruenceSubgroups true
gptkbp:hasGenerators S = [[0, -1], [1, 0]]
T = [[1, 1], [0, 1]]
gptkbp:hasSubgroup general linear group of 2x2 integer matrices
special linear group of 2x2 real matrices
https://www.w3.org/2000/01/rdf-schema#label special linear group of 2x2 integer matrices
gptkbp:identityElement 2x2 identity matrix
gptkbp:isDiscreteSubgroupOf gptkb:SL(2,_R)
gptkbp:isFinite true
gptkbp:isFinitelyGenerated true
gptkbp:isNonAbelian true
gptkbp:isPerfect true
gptkbp:isQuotientOf gptkb:modular_group_PSL(2,_Z)
gptkbp:isSolvable true
gptkbp:operator matrix multiplication
gptkbp:order infinite
gptkbp:presentedBy <S, T | S^4 = I, (ST)^3 = I>
gptkbp:relatedTo gptkb:SL(2,_R)
gptkb:PSL(2,_Z)
modular group
GL(2, Z)
gptkbp:bfsParent gptkb:SL(2,ℤ)
gptkbp:bfsLayer 6