noncommutative tori
E959834
UNEXPLORED
Noncommutative tori are fundamental examples of noncommutative spaces in operator algebras and noncommutative geometry, generalizing the algebra of functions on a classical torus by deforming the commutation relations of its coordinate functions.
All labels observed (1)
| Label | Occurrences |
|---|---|
| noncommutative tori canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T12027031 — 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: noncommutative tori Context triple: [Noncommutative Geometry (1994 book), subject, noncommutative tori]
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A.
noncommutative geometry
Noncommutative geometry is a branch of mathematics that generalizes geometric concepts to settings where coordinate algebras do not commute, with deep applications in operator algebras, topology, and theoretical physics.
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B.
C*-algebras
C*-algebras are a class of norm-closed, self-adjoint operator algebras on Hilbert spaces that form a fundamental framework in functional analysis and noncommutative geometry.
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C.
Connes–Moscovici index theorem
The Connes–Moscovici index theorem is a fundamental result in noncommutative geometry that generalizes the classical Atiyah–Singer index theorem to the setting of foliations and noncommutative spaces.
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D.
von Neumann algebras
Von Neumann algebras are operator algebras of bounded operators on a Hilbert space that are closed in the weak operator topology and under taking adjoints, forming a central object in functional analysis and quantum theory.
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E.
Noncommutative Geometry, Quantum Fields and Motives
Noncommutative Geometry, Quantum Fields and Motives is a seminal work by Alain Connes that develops a deep interplay between noncommutative geometry, quantum field theory, and arithmetic geometry through the language of motives.
- 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: noncommutative tori Target entity description: Noncommutative tori are fundamental examples of noncommutative spaces in operator algebras and noncommutative geometry, generalizing the algebra of functions on a classical torus by deforming the commutation relations of its coordinate functions.
-
A.
noncommutative geometry
Noncommutative geometry is a branch of mathematics that generalizes geometric concepts to settings where coordinate algebras do not commute, with deep applications in operator algebras, topology, and theoretical physics.
-
B.
C*-algebras
C*-algebras are a class of norm-closed, self-adjoint operator algebras on Hilbert spaces that form a fundamental framework in functional analysis and noncommutative geometry.
-
C.
Connes–Moscovici index theorem
The Connes–Moscovici index theorem is a fundamental result in noncommutative geometry that generalizes the classical Atiyah–Singer index theorem to the setting of foliations and noncommutative spaces.
-
D.
von Neumann algebras
Von Neumann algebras are operator algebras of bounded operators on a Hilbert space that are closed in the weak operator topology and under taking adjoints, forming a central object in functional analysis and quantum theory.
-
E.
Noncommutative Geometry, Quantum Fields and Motives
Noncommutative Geometry, Quantum Fields and Motives is a seminal work by Alain Connes that develops a deep interplay between noncommutative geometry, quantum field theory, and arithmetic geometry through the language of motives.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.