Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:alsoKnownAs |
gptkb:symplectic_Lie_algebra
|
| gptkbp:basisFor |
matrices of size 2n x 2n
|
| gptkbp:Cartan_matrix |
gptkb:C_n
|
| gptkbp:centralTo |
trivial
|
| gptkbp:definedIn |
preserving a non-degenerate skew-symmetric bilinear form
|
| gptkbp:dimensions |
n(2n+1)
|
| gptkbp:field |
F
|
| gptkbp:generation |
Hamiltonian matrices
|
| gptkbp:heldBy |
gptkb:classical_Lie_algebra
|
| https://www.w3.org/2000/01/rdf-schema#label |
sp {2n}(F) (Lie algebra)
|
| gptkbp:rank |
n
arbitrary field F (char ≠ 2) |
| gptkbp:relatedGroup |
Sp_{2n}(F)
|
| gptkbp:structureConstants |
depend on symplectic form
|
| gptkbp:subclassOf |
gl_{2n}(F)
|
| gptkbp:type |
gptkb:C_n
gptkb:Lie_group |
| gptkbp:usedIn |
mathematical physics
representation theory symplectic geometry |
| gptkbp:bfsParent |
gptkb:sp_{2n}(F)
|
| gptkbp:bfsLayer |
7
|