the circle group
E1533731
UNEXPLORED
The circle group is the group of complex numbers of absolute value 1 under multiplication, forming a fundamental example of a compact, abelian Lie group.
All labels observed (1)
| Label | Occurrences |
|---|---|
| the circle group canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T22382108 — 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: the circle group Context triple: [U(1), isIsomorphicTo, the circle group]
-
A.
Selmer group
A Selmer group is an arithmetic invariant in number theory that encodes obstructions to local-global principles for Galois representations or abelian varieties, playing a central role in studying Diophantine equations and Iwasawa theory.
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B.
Pontryagin duality
Pontryagin duality is a fundamental theorem in harmonic analysis and topological group theory that establishes a duality between locally compact abelian groups and their groups of continuous characters.
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C.
Abelian groups
Abelian groups are algebraic structures in which the group operation is commutative, meaning the order of combining elements does not affect the result.
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D.
Weil group
The Weil group is an extension of the absolute Galois group introduced by André Weil to refine class field theory and play a central role in the formulation of the local and global Langlands correspondences.
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E.
Z/2Z
Z/2Z is the cyclic group of order 2, consisting of two elements with addition modulo 2.
- 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: the circle group Target entity description: The circle group is the group of complex numbers of absolute value 1 under multiplication, forming a fundamental example of a compact, abelian Lie group.
-
A.
Selmer group
A Selmer group is an arithmetic invariant in number theory that encodes obstructions to local-global principles for Galois representations or abelian varieties, playing a central role in studying Diophantine equations and Iwasawa theory.
-
B.
Pontryagin duality
Pontryagin duality is a fundamental theorem in harmonic analysis and topological group theory that establishes a duality between locally compact abelian groups and their groups of continuous characters.
-
C.
Abelian groups
Abelian groups are algebraic structures in which the group operation is commutative, meaning the order of combining elements does not affect the result.
-
D.
Weil group
The Weil group is an extension of the absolute Galois group introduced by André Weil to refine class field theory and play a central role in the formulation of the local and global Langlands correspondences.
-
E.
Z/2Z
Z/2Z is the cyclic group of order 2, consisting of two elements with addition modulo 2.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.