Algebres de Jordan libres et representations de sl(2,J)
Bibliographic record
Abstract
<div> Let J be a unital Jordan algebra. When J is the free Jordan algebra J(D) on D generators, a formula for the dimension of its homogeneous components has been conjectured in [22]. Let sl2(J) be the universal central extension of the Tits-Kantor-Koecher Lie algebra T KK(J). In the present paper, we connect the conjecture with the representation theory of sl2(J). For example, we prove the conjecture under the hypothesis that the Lie algebra sl2(J(D)) is F P∞, or if certain modules admit a good filtration. However, most of our results are unconditional. For example, we prove that sl2(J) is finitely presented if J is finitely presented. We also show that the standard modules are finite dimensional. Surprisingly the proofs make use of some deep results of E. Zelmanov. </div>
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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 | 0.005 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| 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".