Triple

T21953417
Position Surface form Disambiguated ID Type / Status
Subject Lie algebra E542122 entity
Predicate hasExample P1259 FINISHED
Object Virasoro algebra
The Virasoro algebra is an infinite-dimensional Lie algebra that plays a central role in two-dimensional conformal field theory and string theory as the symmetry algebra of local conformal transformations.
E1510867 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Virasoro algebra | Statement: [Lie algebra, hasExample, Virasoro algebra]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Virasoro algebra
Context triple: [Lie algebra, hasExample, Virasoro algebra]
  • A. Sugawara construction of the Virasoro algebra
    The Sugawara construction of the Virasoro algebra is a method in two-dimensional conformal field theory that builds the Virasoro generators from currents of an affine Lie algebra, yielding the energy-momentum tensor and central charge in terms of the underlying symmetry.
  • B. Onsager algebra
    The Onsager algebra is an infinite-dimensional Lie algebra introduced in the study of exactly solvable models in statistical mechanics, particularly the two-dimensional Ising model.
  • C. Kac–Moody algebras
    Kac–Moody algebras are a broad class of (generally infinite-dimensional) Lie algebras defined by generalized Cartan matrices, encompassing finite-dimensional semisimple Lie algebras and their infinite-dimensional extensions used in representation theory and mathematical physics.
  • D. Wess–Zumino–Witten model
    The Wess–Zumino–Witten model is a two-dimensional conformal field theory describing interacting scalar fields valued in a Lie group, notable for its topological Wess–Zumino term and applications in string theory and condensed matter physics.
  • E. Knizhnik–Zamolodchikov equations
    The Knizhnik–Zamolodchikov equations are a system of differential equations in conformal field theory that govern correlation functions of Wess–Zumino–Witten models and connect representation theory of affine Lie algebras with braid group monodromy and quantum groups.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Virasoro algebra
Triple: [Lie algebra, hasExample, Virasoro algebra]
Generated description
The Virasoro algebra is an infinite-dimensional Lie algebra that plays a central role in two-dimensional conformal field theory and string theory as the symmetry algebra of local conformal transformations.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Virasoro algebra
Target entity description: The Virasoro algebra is an infinite-dimensional Lie algebra that plays a central role in two-dimensional conformal field theory and string theory as the symmetry algebra of local conformal transformations.
  • A. Sugawara construction of the Virasoro algebra
    The Sugawara construction of the Virasoro algebra is a method in two-dimensional conformal field theory that builds the Virasoro generators from currents of an affine Lie algebra, yielding the energy-momentum tensor and central charge in terms of the underlying symmetry.
  • B. Onsager algebra
    The Onsager algebra is an infinite-dimensional Lie algebra introduced in the study of exactly solvable models in statistical mechanics, particularly the two-dimensional Ising model.
  • C. Kac–Moody algebras
    Kac–Moody algebras are a broad class of (generally infinite-dimensional) Lie algebras defined by generalized Cartan matrices, encompassing finite-dimensional semisimple Lie algebras and their infinite-dimensional extensions used in representation theory and mathematical physics.
  • D. Wess–Zumino–Witten model
    The Wess–Zumino–Witten model is a two-dimensional conformal field theory describing interacting scalar fields valued in a Lie group, notable for its topological Wess–Zumino term and applications in string theory and condensed matter physics.
  • E. Knizhnik–Zamolodchikov equations
    The Knizhnik–Zamolodchikov equations are a system of differential equations in conformal field theory that govern correlation functions of Wess–Zumino–Witten models and connect representation theory of affine Lie algebras with braid group monodromy and quantum groups.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69e0c47ef0e48190a50e1bcc43f4b3fd completed April 16, 2026, 11:14 a.m.
NER Named-entity recognition batch_69f1243dfb4081909bc7a722843ffea7 completed April 28, 2026, 9:18 p.m.
NED1 Entity disambiguation (via context triple) batch_6a0a670672b481908b92e15245212e64 completed May 18, 2026, 1:10 a.m.
NEDg Description generation batch_6a0a67c29848819080860f13b4c9697b completed May 18, 2026, 1:13 a.m.
NED2 Entity disambiguation (via description) batch_6a0a686a0f208190977890119ffcff79 completed May 18, 2026, 1:16 a.m.
Created at: April 16, 2026, 7:59 p.m.