|
gptkbp:instanceOf
|
gptkb:group_of_people
|
|
gptkbp:actsOn
|
symplectic vector space
|
|
gptkbp:application
|
gptkb:algebraic_geometry
gptkb:classical_mechanics
differential geometry
physics
quantum mechanics
representation theory
|
|
gptkbp:category
|
classical group
|
|
gptkbp:centralTo
|
{±I} (for Sp(2n, C))
|
|
gptkbp:compact
|
yes (for Sp(2n, R))
yes (for compact symplectic group)
|
|
gptkbp:connects
|
yes (for Sp(2n, R))
|
|
gptkbp:definedIn
|
preserving a non-degenerate, skew-symmetric bilinear form
|
|
gptkbp:dimensions
|
n(2n+1) for Sp(2n, R)
|
|
gptkbp:field
|
gptkb:mathematics
complex numbers
finite fields
real numbers
|
|
gptkbp:hasConnection
|
yes (for Sp(2n, C))
|
|
gptkbp:hasSubfield
|
gptkb:algebra
gptkb:geometry
|
|
gptkbp:hasSubgroup
|
gptkb:metaplectic_group
gptkb:compact_symplectic_group
gptkb:projective_symplectic_group
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Symplectic group
|
|
gptkbp:isAlgebraicGroup
|
yes
|
|
gptkbp:isMatrixGroup
|
yes
|
|
gptkbp:isReductive
|
yes
|
|
gptkbp:isSimple
|
yes (for n > 1)
|
|
gptkbp:notation
|
gptkb:Sp(2n,_F)
|
|
gptkbp:parameter
|
F (field)
n (positive integer)
|
|
gptkbp:preserves
|
symplectic form
|
|
gptkbp:relatedConcept
|
gptkb:Hamiltonian_mechanics
gptkb:symplectic_Lie_algebra
symplectic manifold
|
|
gptkbp:relatedTo
|
gptkb:general_linear_group
orthogonal group
|
|
gptkbp:studiedBy
|
Elie Cartan
|
|
gptkbp:type
|
gptkb:group_of_people
gptkb:Lie_group
type C
|
|
gptkbp:Weyl_group
|
hyperoctahedral group
|
|
gptkbp:bfsParent
|
gptkb:group_of_people
|
|
gptkbp:bfsLayer
|
4
|