Triple
T21953162
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Cartan–Killing form |
E542117
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | Lie algebra invariant |
C10588
|
CONCEPT FINISHED |
How this triple was built (1 step)
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.
CD
Concept disambiguation
gpt-5-mini-2025-08-07
Target class: Lie algebra invariant Context triple: [Cartan–Killing form, instanceOf, Lie algebra invariant]
-
A.
non-abelian Lie algebra
A non-abelian Lie algebra is a Lie algebra whose Lie bracket is not identically zero on all pairs of elements, meaning there exist elements whose bracket does not commute.
-
B.
Lie algebra generators
Lie algebra generators are the fundamental elements of a Lie algebra whose linear combinations and commutators encode the infinitesimal symmetries and structure constants of a continuous symmetry group.
-
C.
subalgebra of a Lie algebra
A subalgebra of a Lie algebra is a linear subspace that is closed under the Lie bracket, meaning the bracket of any two of its elements remains within the subspace.
-
D.
geometric invariant
chosen
A geometric invariant is a property of a geometric object that remains unchanged under a specified group of transformations, such as rotations, translations, or more general symmetries.
-
E.
object in invariant theory
An object in invariant theory is a mathematical entity, such as a vector space, polynomial ring, or group action, whose structure and symmetries are studied through the functions or quantities that remain unchanged under a specified group of transformations.
- F. None of above.
Provenance (1 batch)
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. |
Created at: April 16, 2026, 7:59 p.m.