Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group orthogonal group |
| gptkbp:actsOn |
2n-dimensional vector space over F
|
| gptkbp:centralTo |
{±I} (if char(F) ≠ 2)
|
| gptkbp:definedIn |
field F
|
| gptkbp:dimensions |
n(2n+1)
|
| gptkbp:hasConnection |
true
|
| gptkbp:hasMaximalSubgroup |
U(n) (if F = C)
|
| gptkbp:hasSubgroup |
GL(2n, F)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Sp(2n, F)
|
| gptkbp:isAlgebraicGroup |
true
|
| gptkbp:isReductive |
true
|
| gptkbp:isSimple |
true (for n > 1 and char(F) ≠ 2)
|
| gptkbp:Lie_algebra |
gptkb:sp(2n,_F)
|
| gptkbp:notation |
Sp_{2n}(F)
|
| gptkbp:order |
2^{n^2} \\prod_{i=1}^n (q^{2i}-1) (if F=F_q, finite field)
|
| gptkbp:preserves |
non-degenerate skew-symmetric bilinear form
|
| gptkbp:realForm |
Sp(2n, C) (if F = R)
|
| gptkbp:type |
C_n (in Cartan classification)
|
| gptkbp:Weyl_group |
hyperoctahedral group
|
| gptkbp:bfsParent |
gptkb:orthogonal_group
gptkb:Symplectic_group |
| gptkbp:bfsLayer |
5
|