symplectic group Sp(2n,R)

E1436555 UNEXPLORED

The symplectic group Sp(2n,ℝ) is the Lie group of 2n×2n real matrices that preserve a nondegenerate skew-symmetric bilinear form, playing a central role in symplectic geometry and Hamiltonian mechanics.

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All labels observed (5)

Label	Occurrences
symplectic group	3
real symplectic group Sp(2g,R)	1
symplectic group Sp(2g, R)	1
symplectic group Sp(2g,ℤ)	1
symplectic group Sp(2n,R) canonical	1

How this entity was disambiguated

This entity first appeared as the object of triple T20509541 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: symplectic group Sp(2n,R)
Context triple: [Heisenberg Lie algebra, hasAutomorphismGroupContaining, symplectic group Sp(2n,R)]

A. SL(2,R)
SL(2,R) is the Lie group of 2×2 real matrices with determinant 1, fundamental in representation theory, geometry, and the study of symmetries in mathematics and physics.
B. special orthogonal group SO(n)
The special orthogonal group SO(n) is the group of all n×n real rotation matrices with determinant 1, representing orientation-preserving isometries of n-dimensional Euclidean space that fix the origin.
C. special linear group SL(n,R)
The special linear group SL(n,ℝ) is the Lie group of all n×n real matrices with determinant 1, fundamental in linear algebra and differential geometry as the group of volume-preserving linear transformations.
D. Spin(2,d)
Spin(2,d) is the double-covering spin group of SO(2,d), serving as the relevant symmetry group for spinor fields in (d+1)-dimensional anti-de Sitter space.
E. SL(2,C)
SL(2,C) is the complex special linear group of 2×2 matrices with determinant 1, which serves as the double cover and spinor representation group of the proper orthochronous Lorentz group in four-dimensional spacetime.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: symplectic group Sp(2n,R)
Target entity description: The symplectic group Sp(2n,ℝ) is the Lie group of 2n×2n real matrices that preserve a nondegenerate skew-symmetric bilinear form, playing a central role in symplectic geometry and Hamiltonian mechanics.

A. SL(2,R)
SL(2,R) is the Lie group of 2×2 real matrices with determinant 1, fundamental in representation theory, geometry, and the study of symmetries in mathematics and physics.
B. special orthogonal group SO(n)
The special orthogonal group SO(n) is the group of all n×n real rotation matrices with determinant 1, representing orientation-preserving isometries of n-dimensional Euclidean space that fix the origin.
C. special linear group SL(n,R)
The special linear group SL(n,ℝ) is the Lie group of all n×n real matrices with determinant 1, fundamental in linear algebra and differential geometry as the group of volume-preserving linear transformations.
D. Spin(2,d)
Spin(2,d) is the double-covering spin group of SO(2,d), serving as the relevant symmetry group for spinor fields in (d+1)-dimensional anti-de Sitter space.
E. SL(2,C)
SL(2,C) is the complex special linear group of 2×2 matrices with determinant 1, which serves as the double cover and spinor representation group of the proper orthochronous Lorentz group in four-dimensional spacetime.
F. None of above. chosen