special linear group SL(n,q)

URI: https://gptkb.org/entity/special_linear_group_SL(n,q)
GPTKB entity
Statements (26)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
gptkb:Lie_group
gptkbp:actsOn vector space of dimension n over field of order q
gptkbp:centralTo scalar matrices with determinant 1
gptkbp:containsElement n x n matrices
gptkbp:definedIn finite field of order q
gptkbp:elementsHaveDeterminant 1
gptkbp:finiteIf q is finite
gptkbp:generation elementary matrices
gptkbp:hasSubgroup gptkb:general_linear_group_GL(n,q)
gptkbp:infiniteIf q is infinite
gptkbp:isSimple n >= 2, (n,q) ≠ (2,2), (2,3)
gptkbp:namedAfter gptkb:orthogonal_group
gptkbp:notation gptkb:SL(n,q)
gptkbp:order q^{n^2-1} * product_{k=2}^n (q^k-1)
gptkbp:relatedGroup matrix multiplication
gptkbp:relatedTo gptkb:projective_special_linear_group_PSL(n,q)
gptkbp:studiedBy gptkb:Ferdinand_Georg_Frobenius
gptkbp:usedIn gptkb:algebraic_geometry
gptkb:geometry
group theory
number theory
representation theory
gptkbp:bfsParent gptkb:Chevalley_groups
gptkbp:bfsLayer 8
https://www.w3.org/2000/01/rdf-schema#label special linear group SL(n,q)