Weak amenability of Fourier algebras and local synthesis of the\n anti-diagonal
Bibliographic record
Abstract
We show that for a connected Lie group $G$, its Fourier algebra $A(G)$ is\nweakly amenable only if $G$ is abelian. Our main new idea is to show that weak\namenability of $A(G)$ implies that the anti-diagonal,\n$\\check{\\Delta}_G=\\{(g,g^{-1}):g\\in G\\}$, is a set of local synthesis for\n$A(G\\times G)$. We then show that this cannot happen if $G$ is non-abelian. We\nconclude for a locally compact group $G$, that $A(G)$ can be weakly amenable\nonly if it contains no closed connected non-abelian Lie subgroups. In\nparticular, for a Lie group $G$, $A(G)$ is weakly amenable if and only if its\nconnected component of the identity $G_e$ is abelian.\n
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".