Bibliographic record
Abstract
We classify central extensions of Artin-Schelter regular algebras of global dimension atmost 3, generated by elements of degree 1.Let 𝐴 be a quadratic Artin-Schelter regular algebra generated by degree 1 elements over a field 𝑘, and let 𝐷 be an extension of 𝐴 by a central element 𝑧, such that 𝐴 ≅ 𝐷/⟨𝑧⟩.The study by Le Bruyn, S.P. Smith, Van den Bergh "Central extensions of three dimensional Artin-Schelter regular algebra" [13] is cited as the primary source of information in this thesis.Le Bruyn et al. used the fact that the quadratic algebras under specific conditions are Koszul to analyze the central extensions of three dimensional Artin-Schelter regular algebras.Adopting the same facts, we identify central extensions of one dimensional and two dimensional Artin-Schelter regular algebra generated by degree 1 elements.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 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 | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".