Associative algebras for (logarithmic) twisted modules for a vertex operator algebra
Bibliographic record
Abstract
We construct two associative algebras from a vertex operator algebra V V and a general automorphism g g of V V . The first, called a g g -twisted zero-mode algebra, is a subquotient of what we call a g g -twisted universal enveloping algebra of V V . These algebras are generalizations of the corresponding algebras introduced and studied by Frenkel-Zhu and Nagatomo-Tsuchiya in the (untwisted) case that g g is the identity. The other is a generalization of the g g -twisted version of Zhu’s algebra for suitable g g -twisted modules constructed by Dong-Li-Mason when the order of g g is finite. We are mainly interested in g g -twisted V V -modules introduced by the first author in the case that g g is of infinite order and does not act on V V semisimply. In this case, twisted vertex operators in general involve the logarithm of the variable. We construct functors between categories of suitable modules for these associative algebras and categories of suitable (logarithmic) g g -twisted V V -modules. Using these functors, we prove that the g g -twisted zero-mode algebra and the g g -twisted generalization of Zhu’s algebra are in fact isomorphic.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.017 | 0.005 |
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".