Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:Cartan_matrix |
gptkb:C_n
|
| gptkbp:centralTo |
trivial (for n > 1)
|
| gptkbp:classicalLieAlgebra |
yes
|
| gptkbp:definedIn |
preserving symplectic form
|
| gptkbp:dimensions |
n(2n+1)
|
| gptkbp:field |
F
|
| gptkbp:fullName |
gptkb:symplectic_Lie_algebra
|
| https://www.w3.org/2000/01/rdf-schema#label |
sp(2n, F)
|
| gptkbp:isSemisimple |
yes
|
| gptkbp:isSimple |
yes (for n > 1)
|
| gptkbp:matrixRealization |
2n x 2n matrices
|
| gptkbp:rank |
n
|
| gptkbp:relatedGroup |
gptkb:Sp(2n,_F)
|
| gptkbp:structureConstants |
depend on symplectic form
|
| gptkbp:type |
gptkb:C_n
gptkb:Lie_group |
| gptkbp:usedIn |
mathematical physics
representation theory symplectic geometry |
| gptkbp:bfsParent |
gptkb:symplectic_Lie_algebra
gptkb:Sp(2n,_F) |
| gptkbp:bfsLayer |
6
|