U(1)
E553299
U(1) is the group of complex numbers with absolute value 1 under multiplication, commonly representing the symmetry group of electromagnetism and other abelian gauge theories.
All labels observed (2)
| Label | Occurrences |
|---|---|
| U(1) canonical | 5 |
| U(1)_Y gauge group | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5877559 — 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: U(1) Context triple: [Schwinger model, gaugeGroup, U(1)]
-
A.
U1
U1 is one of Berlin’s oldest and most central U-Bahn lines, running predominantly east–west through inner-city districts and serving key cultural and nightlife areas.
-
B.
U1
U1 is a major line of the Nuremberg U-Bahn rapid transit system, connecting key districts across the Nuremberg metropolitan area.
-
C.
the U
The U is a common nickname for the University of Utah, a major public research university located in Salt Lake City.
-
D.
SU(3)
SU(3) is the special unitary group of degree three, a Lie group fundamental to the mathematical description of the strong interaction and the classification of hadrons in particle physics.
-
E.
UJ
UJ is a major public university in Johannesburg, South Africa, known for its diverse academic programs and strong focus on research and innovation.
- 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: U(1) Target entity description: U(1) is the group of complex numbers with absolute value 1 under multiplication, commonly representing the symmetry group of electromagnetism and other abelian gauge theories.
-
A.
U1
U1 is one of Berlin’s oldest and most central U-Bahn lines, running predominantly east–west through inner-city districts and serving key cultural and nightlife areas.
-
B.
U1
U1 is a major line of the Nuremberg U-Bahn rapid transit system, connecting key districts across the Nuremberg metropolitan area.
-
C.
the U
The U is a common nickname for the University of Utah, a major public research university located in Salt Lake City.
-
D.
SU(3)
SU(3) is the special unitary group of degree three, a Lie group fundamental to the mathematical description of the strong interaction and the classification of hadrons in particle physics.
-
E.
UJ
UJ is a major public university in Johannesburg, South Africa, known for its diverse academic programs and strong focus on research and innovation.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
abelian group
ⓘ
mathematical group ⓘ one-parameter Lie group ⓘ topological group ⓘ unitary group ⓘ |
| appearsIn |
abelian gauge theories
ⓘ
electromagnetism ⓘ quantum electrodynamics ⓘ |
| hasAlternativeName | circle group ⓘ |
| hasAlternativeNotation | T ⓘ |
| hasCenter | itself ⓘ |
| hasCharacterGroup | Z ⓘ |
| hasChargeQuantizationLabeledBy | integers in many models ⓘ |
| hasCoveringSpace | R with projection \theta \mapsto e^{i\theta} ⓘ |
| hasDefinition | group of complex numbers with absolute value 1 under multiplication ⓘ |
| hasDimension | 1 ⓘ |
| hasElementForm | e^{i\theta} with real \theta ⓘ |
| hasFundamentalGroup | Z ⓘ |
| hasHaarMeasure | normalized Lebesgue measure on the circle ⓘ |
| hasIdentityElement | 1 ⓘ |
| hasInverseOperation | complex conjugation ⓘ |
| hasIrreducibleRepresentationsLabeledBy | integers ⓘ |
| hasLieAlgebra | iR ⓘ |
| hasLieAlgebraDimension | 1 ⓘ |
| hasManifoldStructure | 1-dimensional smooth manifold ⓘ |
| hasOperation | complex multiplication ⓘ |
| hasPontryaginDual | Z ⓘ |
| hasRepresentationTheory | all continuous irreducible unitary representations are 1-dimensional ⓘ |
| hasTopology | subspace topology from C ⓘ |
| isAbelian | true ⓘ |
| isCommutativeLieGroup | true ⓘ |
| isCompact | true ⓘ |
| isConnected | true ⓘ |
| isGaugeGroupOf |
QED
ⓘ
linked to:
quantum electrodynamics
electromagnetic interaction ⓘ |
| isHausdorff | true ⓘ |
| isHomeomorphicTo | S^1 ⓘ |
| isIsomorphicTo |
R/Z
ⓘ
SO(2) ⓘ
linked to:
special orthogonal group SO(n)
the circle group ⓘ |
| isLocallyCompact | true ⓘ |
| isMaximalTorusIn |
SU(2)
ⓘ
U(n) ⓘ |
| isPathConnected | true ⓘ |
| isSimpleConnected | false ⓘ |
| isUnitaryGroupOf | 1-dimensional complex Hilbert space ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: U(1) Description of subject: U(1) is the group of complex numbers with absolute value 1 under multiplication, commonly representing the symmetry group of electromagnetism and other abelian gauge theories.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.