On the module structure of the center of hyperelliptic Krichever–Novikov algebras II
Bibliographic record
Abstract
Let R=C[t±1,u:u2=t(t−α1)⋯(t−α2n)], corresponding to a nonsingular hyperelliptic curve. Let g⊗R be the corresponding current Lie algebra. The universal central extension of g⊗R is ĝ=g⊗R⊕ΩR/dR, where ΩR/dR is a module over Aut(R). In earlier work, Cox–Im described how ΩR/dR decomposes into a direct sum of irreducible representations when Aut(R) was the cyclic group C2k or the dihedral group D2k. In this paper, we precisely determine Aut(R), giving examples of 2n-tuples (α1,…,α2n) when Aut(R) is Gn=Dicn,Un≅D2n, or Un (n even). We then describe the decomposition of ΩR/dR when Aut(R) is D2k.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".