Gradings and contractions of affine Kac–Moody algebras
Bibliographic record
Abstract
We study contractions of affine Kac–Moody algebras (KMAs) with respect to their twisted and untwisted Kac–Moody subalgebras and also contract twisted KMA with respect to their affine subalgebras. Our work generalizes the Inönü–Wigner contraction of KMA by Majumdar [J. Math. Phys. 34, 2059 (1993)] in several directions. We compare Inönü–Wigner contractions with respect to twisted subalgebras to another kind of contractions, which we call modulo contractions. We also introduce a novel type of contractions, based on Z-gradings of KMA, which we call level contractions. Along the way we use an algorithm for constructing “Kac–Moody–like algebras” ĝ for any (and not just semisimple) finite-dimensional Lie algebra g.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".