Levi Decomposable Subalgebras of Classical Lie Algebras With Regular Simple Levi Factor
Bibliographic record
Abstract
This thesis describes and characterizes a significant class of subalgebras of the classical Lie algebras, namely those which are Levi decomposable with regular and simple Levi factor, with select exceptions. Such subalgebras are entirely determined by their Levi factors and radicals. The possible Levi factors are well-established in the literature and so the contribution of this thesis is a characterization of the radicals. The radicals naturally decompose into nontrivial and trivial components. The nontrivial component is found to be fully classified by subsets of the parent root system and Weyl group. However, a classification of the trivial component requires solving the open problem of classifying solvable subalgebras of classical Lie algebras. Nonetheless, this thesis establishes a criterion on the trivial components for determining when two such subalgebras are conjugate. This thesis also briefly explores the ramifications of relaxing simplicity of the Levi factor to allow for semisimplicity.
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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) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.022 | 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; both teacher heads agree on what is shown here.
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".