Triple

T12095290
Position Surface form Disambiguated ID Type / Status
Subject Jacques Dixmier E288055 entity
Predicate notableWork P4 FINISHED
Object Algèbres enveloppantes E542123 NE FINISHED

How this triple was built (2 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: Algèbres enveloppantes | Statement: [Jacques Dixmier, notableWork, Algèbres enveloppantes]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Algèbres enveloppantes
Context triple: [Jacques Dixmier, notableWork, Algèbres enveloppantes]
  • A. universal enveloping algebras chosen
    Universal enveloping algebras are associative algebras that encode the structure of Lie algebras and allow Lie-theoretic problems to be studied using tools from associative and representation theory.
  • 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. Lie algebras
    Lie algebras are algebraic structures used to study continuous symmetries, especially those arising from Lie groups, via a linearized, infinitesimal perspective.
  • D. Gelfand–Kirillov dimension
    The Gelfand–Kirillov dimension is an invariant in noncommutative algebra that measures the growth rate of algebras and modules, serving as an analogue of Krull dimension for noncommutative settings.
  • E. Weyl algebra
    The Weyl algebra is a fundamental noncommutative algebra generated by position and momentum operators satisfying canonical commutation relations, central in quantum mechanics and representation theory.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69d6ab4964708190850585628b287b0c completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d91550ce508190babf5755e1553734 completed April 10, 2026, 3:20 p.m.
NED1 Entity disambiguation (via context triple) batch_69f5f66edf7881908f29b5b40b9d020f completed May 2, 2026, 1:04 p.m.
Created at: April 8, 2026, 9:48 p.m.