Embedding of “open” superalgebras into affine Kac–Moody superalgebras
Bibliographic record
Abstract
We define the concepts of open Lie superalgebras and their closure and study their embedding into affine Kac–Moody (KM) superalgebras. We distinguish between two types of open algebras, whose closures typically yield twisted or untwisted KM superalgebras. We show that the open dynamical symmetry superalgebra S0 of the Dirac theory of the Taub–NUT model, studied by Cotăescu and Visinescu [J. Phys. A 40, 11987 (2007)], cannot be embedded into a twisted KM superalgebra, in contrast to their claim. Our analysis of the above relativistic model reveals the deeper reason of why the hydrogen algebras HN, studied by Daboul and Slodowy, must be “twisted-like” (genuinely and not-genuinely twisted) KM subalgebras.
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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 | 0.001 | 0.001 |
| 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 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".