Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:actsOn |
F^{2n}
|
| gptkbp:centralTo |
scalar matrices λI with λ in F^*
|
| gptkbp:consistsOf |
invertible 2n×2n matrices over F
|
| gptkbp:contains |
SL_{2n}(F)
|
| gptkbp:contains_as_subgroups |
GL_{k}(F) for k ≤ 2n
|
| gptkbp:definedIn |
field F
|
| gptkbp:determinant_map |
GL_{2n}(F) → F^*
|
| gptkbp:dimensions |
(2n)^2
|
| gptkbp:hasSubgroup |
GL_{m}(F) (for m ≥ 2n)
|
| https://www.w3.org/2000/01/rdf-schema#label |
GL {2n}(F)
|
| gptkbp:identityElement |
identity matrix I_{2n}
|
| gptkbp:is_a_classical_group |
yes
|
| gptkbp:is_a_Lie_group_if |
F = R or C
|
| gptkbp:is_a_linear_group |
yes
|
| gptkbp:is_a_reductive_group |
yes
|
| gptkbp:isNonAbelian |
yes
|
| gptkbp:order_(if_F_is_finite) |
product_{k=0}^{2n-1} (|F|^{2n} - |F|^k)
|
| gptkbp:quotient_by_center |
PGL_{2n}(F)
|
| gptkbp:bfsParent |
gptkb:sp_{2n}(F)
|
| gptkbp:bfsLayer |
7
|