Bibliographic record
Abstract
The search for an appropriate notion of amenability for inverse semigroups is an ongoing program in operator algebras and related fields.This thesis presents an approach to this problem using the theory of inverse semigroup actions.An inverse semigroup action S ↷ α X is said to be amenable if the action groupoid S ⋉ α X is amenable as an étale groupoid.We prove two fundamental results from the literature on amenable inverse semigroup actions: firstly, that all actions of an inverse semigroup S are amenable whenever the universal action S ↷ θ ÊS 0 is amenable; and secondly, that the universal action of an inverse semigroup S is amenable whenever S admits an idempotent-pure partial homomorphism into an amenable group.These results are applied to show that all actions of graph inverse semigroups and abelian inverse semigroups are amenable, and to show that the universal action of the free inverse semigroup on two generators is not amenable.We also introduce an intrinsic action of an inverse semigroup on its Stone-Čech compactification, give an inverse semigroup model for Willett's HLS groupoids, and produce an example of an inverse semigroup W which witnesses weak containment but fails to have an amenable universal action.i
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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".