Triple

T17661263
Position Surface form Disambiguated ID Type / Status
Subject affine Lie algebras E440255 entity
Predicate appearsIn P795 FINISHED
Object Kac’s book Infinite Dimensional Lie Algebras — NE NERFINISHED

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: Kac’s book Infinite Dimensional Lie Algebras | Statement: [affine Lie algebras, appearsIn, Kac’s book Infinite Dimensional Lie Algebras]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Kac’s book Infinite Dimensional Lie Algebras
Context triple: [affine Lie algebras, appearsIn, Kac’s book Infinite Dimensional Lie Algebras]
  • A. affine Lie algebras chosen
    Affine Lie algebras are infinite-dimensional extensions of finite-dimensional simple Lie algebras that play a central role in representation theory, conformal field theory, and the study of exactly solvable models in mathematical physics.
  • B. Lie algebras
    Lie algebras are algebraic structures used to study continuous symmetries, especially those arising from Lie groups, via a linearized, infinitesimal perspective.
  • C. Gel'fand–Kirillov conjecture
    The Gel'fand–Kirillov conjecture is a statement in noncommutative algebra proposing that certain universal enveloping algebras of Lie algebras are birationally equivalent to Weyl algebras, linking their structure to that of algebras of differential operators.
  • D. Drinfeld–Jimbo quantum groups
    Drinfeld–Jimbo quantum groups are deformations of universal enveloping algebras of Lie algebras that provide a foundational algebraic framework for quantum integrable systems and modern representation theory.
  • E. The Classical Groups: Their Invariants and Representations
    The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69d8b9e87e18819087104a44dc4dc5b1 completed April 10, 2026, 8:50 a.m.
NER Named-entity recognition batch_69e46ea67f8081909da164ca21a98675 completed April 19, 2026, 5:56 a.m.
Created at: April 10, 2026, 9:43 a.m.