Triple
T21953416
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Lie algebra |
E542122
|
entity |
| Predicate | hasExample |
P1259
|
FINISHED |
| Object | Witt algebra |
—
|
NE NERFINISHED |
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: Witt algebra | Statement: [Lie algebra, hasExample, Witt algebra]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Witt algebra Context triple: [Lie algebra, hasExample, Witt algebra]
-
A.
affine Lie algebras
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.
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.
-
C.
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.
-
D.
Weyl group
A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory and geometry.
-
E.
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.
- 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: Witt algebra Target entity description: The Witt algebra is an infinite-dimensional Lie algebra of derivations of the Laurent polynomial ring, playing a central role in conformal field theory and as the centerless version of the Virasoro algebra.
-
A.
affine Lie algebras
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.
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.
-
C.
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.
-
D.
Weyl group
A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory and geometry.
-
E.
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.
- F. None of above. chosen
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_69e0c47ef0e48190a50e1bcc43f4b3fd |
completed | April 16, 2026, 11:14 a.m. |
| NER | Named-entity recognition | batch_69f1243dfb4081909bc7a722843ffea7 |
completed | April 28, 2026, 9:18 p.m. |
Created at: April 16, 2026, 7:59 p.m.