Courant algebroid
E1576271
UNEXPLORED
A Courant algebroid is a geometric structure generalizing Lie algebroids that combines a vector bundle with a bracket, anchor map, and bilinear form, and plays a central role in generalized complex geometry and string theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Courant algebroid canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T23234994 — 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: Courant algebroid Context triple: [Lie algebroid, relatedConcept, Courant algebroid]
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A.
Lie algebroid
A Lie algebroid is a geometric structure that generalizes Lie algebras and tangent bundles, encoding infinitesimal symmetries on manifolds via a vector bundle with a Lie bracket and an anchor map.
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B.
Jacobi manifold
A Jacobi manifold is a smooth manifold equipped with a Lie bracket on its space of smooth functions that satisfies a generalized Leibniz rule, extending the notion of Poisson manifolds.
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C.
Poisson geometry
Poisson geometry is the branch of differential geometry that studies manifolds equipped with a Poisson bracket, generalizing classical Hamiltonian mechanics and symplectic geometry.
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D.
Jacobi bracket
The Jacobi bracket is a bilinear operation generalizing the Poisson bracket in differential geometry, central to the theory of Jacobi manifolds and Hamiltonian systems.
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E.
Carathéodory–Jacobi–Lie theorem
The Carathéodory–Jacobi–Lie theorem is a fundamental result in symplectic geometry and Hamiltonian mechanics that provides canonical local coordinates adapted to a given set of commuting functions.
- 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: Courant algebroid Target entity description: A Courant algebroid is a geometric structure generalizing Lie algebroids that combines a vector bundle with a bracket, anchor map, and bilinear form, and plays a central role in generalized complex geometry and string theory.
-
A.
Lie algebroid
A Lie algebroid is a geometric structure that generalizes Lie algebras and tangent bundles, encoding infinitesimal symmetries on manifolds via a vector bundle with a Lie bracket and an anchor map.
-
B.
Jacobi manifold
A Jacobi manifold is a smooth manifold equipped with a Lie bracket on its space of smooth functions that satisfies a generalized Leibniz rule, extending the notion of Poisson manifolds.
-
C.
Poisson geometry
Poisson geometry is the branch of differential geometry that studies manifolds equipped with a Poisson bracket, generalizing classical Hamiltonian mechanics and symplectic geometry.
-
D.
Jacobi bracket
The Jacobi bracket is a bilinear operation generalizing the Poisson bracket in differential geometry, central to the theory of Jacobi manifolds and Hamiltonian systems.
-
E.
Carathéodory–Jacobi–Lie theorem
The Carathéodory–Jacobi–Lie theorem is a fundamental result in symplectic geometry and Hamiltonian mechanics that provides canonical local coordinates adapted to a given set of commuting functions.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.