Isotopy for Extended Affine Lie Algebras and Lie Tori
Bibliographic record
Abstract
Centreless Lie tori have been used by E. Neher to construct all extended affine Lie algebras (EALAs). In this article, we study isotopy for centreless Lie tori, and show that Neher’s construction provides a 1–1 correspondence between centreless Lie tori up to isotopy and families of EALAs up to isomorphism. Also, centreless Lie tori can be coordinatized by unital algebras that are in general nonassociative, and, for many types of centreless Lie tori, there are classical definitions of isotopy for the coordinate algebras. We show for those types that an isotope of a Lie torus is coordinatized by an isotope of its coordinate algebra, thereby connecting the two notions of isotopy. In writing the article, we have not assumed prior knowledge of the theories of EALAs, Lie tori or isotopy.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".