Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:definedIn |
field F
|
| gptkbp:dimensions |
n(2n+1)
|
| gptkbp:Dynkin_diagram |
gptkb:C_n
|
| gptkbp:field |
gptkb:algebra
gptkb:mathematics representation theory |
| gptkbp:hasCartanSubalgebra |
true
|
| https://www.w3.org/2000/01/rdf-schema#label |
symplectic Lie algebra
|
| gptkbp:isClassicalLieAlgebra |
true
|
| gptkbp:isMatrixLieAlgebra |
true
|
| gptkbp:isReductive |
true
|
| gptkbp:isSemisimple |
true
|
| gptkbp:isSimple |
true
|
| gptkbp:notation |
gptkb:sp(2n,_F)
gptkb:sp_{2n}(F) |
| gptkbp:preserves |
symplectic form
|
| gptkbp:realForm |
gptkb:complex_symplectic_Lie_algebra
|
| gptkbp:relatedTo |
gptkb:Hamiltonian_mechanics
differential geometry quantum mechanics orthogonal group |
| gptkbp:subclassOf |
gptkb:general_linear_Lie_algebra
|
| gptkbp:type |
type C_n
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
gptkb:theoretical_physics |
| gptkbp:Weyl_group |
hyperoctahedral group
|
| gptkbp:bfsParent |
gptkb:Symplectic_group
|
| gptkbp:bfsLayer |
5
|