Bibliographic record
Abstract
Let G be a locally compact group. The question of whether H1 L1(G),M(G), the first Hochschild cohomology group of L1(G) with coefficients in M(G), is zero was first studied by B. E. Johnson and initiated his development of the theory of amenable Banach algebras. He was able to show that H1(L1(G), M(G) = 0 whenever G is amenable, a [SIN]-group, or a matrix group satisfying certain conditions. No group such that H1(L1(G),M(G) ≠ 0 is known. In this paper, we approach the problem of whether H1(L1(G),M(G) = 0 from several angles. Using weakly almost periodic functions, we show that H1(L1(G),L1(G) is always Hausdorff for unimodular G. We also show that for [IN]-groups, every derivation D : L1(Gto L1(G is implemented, not necessarily by an element of M(G), but at least by an element of VN(G), the group von Neumann algebra of G. This applies, in particular, to the group G : = T2 ⋊ SL(2,Z}, for which it is unknown whether H}1(L1(G),M(G) = 0. Finally, we analyse the structure of derivations on L1(G); an important role is played by the closed normal subgroup N of G generated by the elements of G with relatively compact conjugacy classes. We can write an arbitrary derivation D : L1(G) to L1(G) as a sum D = DN DN⊥$, where DN and DN⊥ can be tackled with different techniques. Under suitable conditions, all satisfied by T2 ⋊ SL(2,Z}, we can show that DN is implemented by an element of VN(G) and that DN⊥ is implemented by a measure. 1991 Mathematics Subject Classification: 22D05, 22D25, 43A10, 43A20, 46H25, 46L10, 46M20, 47B47, 47B48.
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 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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".