The Structure of H-(co)module Lie algebras
Bibliographic record
Abstract
Let L be a finite dimensional Lie algebra over a field of characteristic 0 .Then by the original Levi theorem, L = B R where R is the solvable radical and B is some maximal semisimple subalgebra.We prove that if L is an H -(co)module algebra for a finite dimensional (co)semisimple Hopf algebra H , then R is H -(co)invariant and B can be chosen to be H -(co)invariant too.Moreover, the nilpotent radical N of L is H -(co)invariant and there exists an H -sub(co)module S R such that R = S N and [B, S] = 0 .In addition, the H -(co)invariant analog of the Weyl theorem is proved.In fact, under certain conditions, these results hold for an H -comodule Lie algebra L , even if H is infinite dimensional.In particular, if L is a Lie algebra graded by an arbitrary group G, then B can be chosen to be graded, and if L is a Lie algebra with a rational action of a reductive affine algebraic group G by automorphisms, then B can be chosen to be G-invariant.Also we prove that every finite dimensional semisimple H -(co)module Lie algebra over a field of characteristic 0 is a direct sum of its minimal H -(co)invariant ideals.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".