Triple

T27176472
Position Surface form Disambiguated ID Type / Status
Subject sl(2,C) E683055 entity
Predicate universalEnvelopingAlgebra P163476 FINISHED
Object U(sl(2,C))
U(sl(2,C)) is the universal enveloping algebra of the complex Lie algebra sl(2,C), serving as a fundamental associative algebra that encodes all its representations and underlies much of the structure in Lie theory and representation theory.
 E1759984 NE FINISHED

How this triple was built (3 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: U(sl(2,C)) | Statement: [sl(2,C), universalEnvelopingAlgebra, U(sl(2,C))]
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: U(sl(2,C))
Triple: [sl(2,C), universalEnvelopingAlgebra, U(sl(2,C))]
Generated description
U(sl(2,C)) is the universal enveloping algebra of the complex Lie algebra sl(2,C), serving as a fundamental associative algebra that encodes all its representations and underlies much of the structure in Lie theory and representation theory.
PD Predicate disambiguation gpt-5-mini-2025-08-07 
Target predicate: universalEnvelopingAlgebra
Context triple: [sl(2,C), universalEnvelopingAlgebra, U(sl(2,C))]
  • A. symmetryAlgebraOf
    Indicates that one entity is the symmetry algebra associated with, or governing the symmetries of, the other entity.
  • B. hasLieAlgebra
    Indicates that one mathematical structure is associated with, or gives rise to, a specific Lie algebra capturing its infinitesimal or tangent-level structure.
  • C. CartanFormula
    Indicates how a derivation or differential operator acts on a product, expressing the result as a graded Leibniz rule that distributes over the product with appropriate signs.
  • D. isComplexificationOf
    Indicates that one entity is a more complex or elaborated version derived from another, simpler entity.
  • E. associatedGradedIs
    Indicates that one mathematical object is the associated graded object (e.g., graded structure derived from a filtration) of another.
  • F. None of above. chosen

Provenance (7 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_69eefad086808190ab89816c0c300476 completed April 27, 2026, 5:57 a.m.
NER Named-entity recognition batch_69f638d11c988190af7fd4572b08e038 completed May 2, 2026, 5:48 p.m.
NED1 Entity disambiguation (via context triple) batch_6a12538af05481908b8108b8b171beb5 completed May 24, 2026, 1:25 a.m.
NEDg Description generation batch_6a12546f814881908c806a1805b7473d completed May 24, 2026, 1:29 a.m.
NED2 Entity disambiguation (via description) batch_6a12552b0cc88190be6bc59664de20c9 completed May 24, 2026, 1:32 a.m.
PD Predicate disambiguation batch_69f63709e4848190b5cf322e06b23fb6 completed May 2, 2026, 5:40 p.m.
PDg Predicate description generation batch_69f638344b148190bf0414ef7c5f1f38 completed May 2, 2026, 5:45 p.m.
Created at: April 27, 2026, 9:26 a.m.