symplectic group over complex numbers
GPTKB entity
Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:actsOn |
complex symplectic vector space
|
| gptkbp:appearsIn |
gptkb:algebraic_geometry
mathematical physics representation theory |
| gptkbp:centralTo |
{±I}
|
| gptkbp:definedIn |
preserving symplectic form
|
| gptkbp:dimensions |
n(2n+1)
|
| gptkbp:field |
complex numbers
|
| gptkbp:heldBy |
connected
simply connected non-compact reductive simple (for n > 1) |
| https://www.w3.org/2000/01/rdf-schema#label |
symplectic group over complex numbers
|
| gptkbp:Lie_algebra |
gptkb:sp(2n,_C)
|
| gptkbp:notation |
gptkb:Sp(2n,_C)
|
| gptkbp:preserves |
non-degenerate skew-symmetric bilinear form
|
| gptkbp:rank |
n
|
| gptkbp:relatedTo |
gptkb:general_linear_group
gptkb:symplectic_group_over_real_numbers orthogonal group |
| gptkbp:type |
C_n (in Cartan classification)
|
| gptkbp:bfsParent |
gptkb:compact_symplectic_group
|
| gptkbp:bfsLayer |
6
|