Group gradings on classical lie superalgebras
Bibliographic record
Abstract
Assuming the base field is algebraically closed, we classify, up to isomorphism, gradings by arbitrary groups on non-exceptional classical simple Lie superalgebras, excluding those of type A(1, 1), and on finite dimensional superinvolution-simple associative superalgebras. We assume the characteristic to be 0 in the Lie case, and different from 2 in the associative case. Our approach is based on a version of Wedderburn Theorem for graded-simple associative superalgebras satisfying a descending chain condition, which allows us to classify superinvolutions using nondegenerate supersymmetric sesquilinear forms on graded modules over a graded-division superalgebra. To transfer the results from the associative case to the Lie case, we use the duality between G-gradings and b G-actions for finite dimensional universal algebras.
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.005 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.000 | 0.003 |
| 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".