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gptkbp:instanceOf
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gptkb:group_of_people
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|
gptkbp:application
|
gptkb:algebraic_geometry
gptkb:classical_mechanics
differential geometry
physics
quantum mechanics
|
|
gptkbp:centralTo
|
{±I}
|
|
gptkbp:compact
|
Sp(n) is compact over the quaternions
|
|
gptkbp:describes
|
The symplectic group Sp(n) is the group of 2n×2n matrices that preserve a symplectic bilinear form.
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gptkbp:dimensions
|
n(2n+1)
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|
gptkbp:field
|
gptkb:mathematics
group theory
quaternions
representation theory
complex numbers
real numbers
symplectic geometry
|
|
gptkbp:fullName
|
orthogonal group
|
|
gptkbp:hasConnection
|
yes
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
sp(n)
|
|
gptkbp:isNonAbelian
|
yes
|
|
gptkbp:isSimple
|
yes
|
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gptkbp:nonCompactForm
|
Sp(2n, R) is the real symplectic group
|
|
gptkbp:notation
|
gptkb:Sp(n)
|
|
gptkbp:relatedTo
|
gptkb:Hamiltonian_mechanics
gptkb:symplectic_Lie_algebra
gptkb:USp(2n)
gptkb:Sp(2n,_R)
gptkb:Sp(n,_C)
gptkb:symplectic_group_over_finite_fields
gptkb:symplectic_group_over_complex_numbers
gptkb:symplectic_group_over_real_numbers
orthogonal group
symplectic manifold
symplectic form
|
|
gptkbp:type
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:bfsParent
|
gptkb:Sp(n)
gptkb:sp(2n,_C)
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|
gptkbp:bfsLayer
|
7
|