“Quantum Groups”
E884938
foundational work in mathematical physics
foundational work in representation theory
mathematics book
monograph
“Quantum Groups” is a foundational work in mathematical physics and representation theory that introduced the concept of quantum groups, deforming classical Lie groups and algebras and profoundly influencing modern algebra and quantum integrable systems.
All labels observed (1)
| Label | Occurrences |
|---|---|
| “Quantum Groups” canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10773444 — 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: “Quantum Groups” Context triple: [Vladimir Drinfeld, notableWork, “Quantum Groups”]
-
A.
Schur–Weyl duality
Schur–Weyl duality is a fundamental result in representation theory that links representations of the symmetric group and the general linear group via their commuting actions on tensor powers of a vector space.
-
B.
The Poincaré-Birkhoff-Witt theorem in ring theory
"The Poincaré-Birkhoff-Witt theorem in ring theory" is a mathematical work, attributed here to N. G. de Bruijn, that studies and applies the Poincaré–Birkhoff–Witt theorem in the context of associative and Lie-theoretic ring structures.
-
C.
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.
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D.
Representations of groups
Representations of groups is a branch of mathematics that studies how abstract groups can act as linear transformations on vector spaces, typically via homomorphisms into groups of matrices.
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E.
Atiyah–Segal axioms
The Atiyah–Segal axioms are a set of mathematical conditions that rigorously define topological quantum field theories as functorial assignments from geometric data to algebraic structures.
- 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: “Quantum Groups” Target entity description: “Quantum Groups” is a foundational work in mathematical physics and representation theory that introduced the concept of quantum groups, deforming classical Lie groups and algebras and profoundly influencing modern algebra and quantum integrable systems.
-
A.
Schur–Weyl duality
Schur–Weyl duality is a fundamental result in representation theory that links representations of the symmetric group and the general linear group via their commuting actions on tensor powers of a vector space.
-
B.
The Poincaré-Birkhoff-Witt theorem in ring theory
"The Poincaré-Birkhoff-Witt theorem in ring theory" is a mathematical work, attributed here to N. G. de Bruijn, that studies and applies the Poincaré–Birkhoff–Witt theorem in the context of associative and Lie-theoretic ring structures.
-
C.
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.
-
D.
Representations of groups
Representations of groups is a branch of mathematics that studies how abstract groups can act as linear transformations on vector spaces, typically via homomorphisms into groups of matrices.
-
E.
Atiyah–Segal axioms
The Atiyah–Segal axioms are a set of mathematical conditions that rigorously define topological quantum field theories as functorial assignments from geometric data to algebraic structures.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
foundational work in mathematical physics
ⓘ
foundational work in representation theory ⓘ mathematics book ⓘ monograph ⓘ |
| coreConcept |
Hopf algebra structure
ⓘ
antipode ⓘ braid group representations ⓘ comultiplication ⓘ counit ⓘ deformation parameter q ⓘ q-analogues of classical objects ⓘ quantum enveloping algebra U_q(g) ⓘ quasitriangular Hopf algebras ⓘ |
| describes |
deformations of classical Lie algebras
ⓘ
deformations of classical Lie groups ⓘ symmetries in quantum integrable models ⓘ |
| field |
algebra
ⓘ
mathematical physics ⓘ quantum integrable systems ⓘ representation theory ⓘ |
| hasNotion |
braided tensor categories
ⓘ
q-characters of representations ⓘ quantum deformation of universal enveloping algebras ⓘ quantum dimensions ⓘ |
| influenceOn |
category theory approaches to quantum algebra
ⓘ
knot invariants ⓘ low-dimensional topology ⓘ modern algebra ⓘ noncommutative geometry ⓘ representation theory of Lie algebras ⓘ representation theory of Lie groups ⓘ theory of quantum integrable systems ⓘ |
| mathematicalArea |
Lie theory
ⓘ
noncommutative algebra ⓘ quantum algebra ⓘ topological quantum field theory ⓘ |
| topic |
Hopf algebras
ⓘ
R-matrices ⓘ Yang–Baxter equation ⓘ deformation of Lie algebras ⓘ deformation of Lie groups ⓘ q-deformations ⓘ quantum groups ⓘ quantum universal enveloping algebras ⓘ |
| usedIn |
construction of quantum invariants of knots and links
ⓘ
exactly solvable models in statistical mechanics ⓘ quantum inverse scattering method ⓘ solutions of the Yang–Baxter equation ⓘ |
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: “Quantum Groups” Description of subject: “Quantum Groups” is a foundational work in mathematical physics and representation theory that introduced the concept of quantum groups, deforming classical Lie groups and algebras and profoundly influencing modern algebra and quantum integrable systems.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.