Bibliographic record
Abstract
We introduce and study the quantum version of the differential operator algebra on Laurent polynomials and its associated Lie algebra over a field F of characteristic 0. The q-quantum torus Fq is the unital associative algebra over F generated by [Formula: see text] subject to the defining relations titj = qi,jtjti, where qi,i = 1, [Formula: see text]. Let D be a subspace of [Formula: see text] where ∂i is the derivation on Fq sending [Formula: see text] to [Formula: see text]. Then, the quantum differential operator algebra is the associative algebra Fq[D]. Assume that Fq[D] is simple as an associative algebra. We compute explicitly all 2-cocycles of Fq[D], viewed as a Lie algebra. More precisely, we show that the second cohomology group of Fq[D] has dimension n if D = 0, dimension 1 if dim D = 1, and dimension 0 if dim D > 1. We also determine all isomorphisms and anti-isomorphisms Fq[D] → Fq′[D′] of simple associative algebras, and all isomorphisms Fq[D]/F → Fq′[D′]/F of simple Lie algebras.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".