Statements (30)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebraic_geometry
gptkb:group_of_people gptkb:Lie_group |
| gptkbp:actsOn |
2n-dimensional complex vector space
|
| gptkbp:appearsIn |
gptkb:algebraic_geometry
mathematical physics representation theory |
| gptkbp:centralTo |
gptkb:Z/2Z
|
| gptkbp:class |
classical group
|
| gptkbp:definedIn |
M^T J M = J, where J is standard symplectic form
|
| gptkbp:dimensions |
n(2n+1)
|
| gptkbp:field |
complex numbers
|
| gptkbp:hasSubgroup |
gptkb:GL(2n,_C)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Sp(2n, C)
|
| gptkbp:Lie_algebra |
gptkb:sp(2n,_C)
|
| gptkbp:maximal_compact_subgroup |
gptkb:USp(2n)
|
| gptkbp:notation |
gptkb:Sp_{2n}(C)
|
| gptkbp:preserves |
non-degenerate skew-symmetric bilinear form
|
| gptkbp:rank |
n
|
| gptkbp:relatedTo |
gptkb:USp(2n)
gptkb:Sp(2n,_R) orthogonal group |
| gptkbp:type |
gptkb:C_n
gptkb:Lie_group connected Lie group simply connected Lie group |
| gptkbp:bfsParent |
gptkb:sp(2n,_C)
gptkb:USp(2n) gptkb:symplectic_group_over_complex_numbers |
| gptkbp:bfsLayer |
7
|