Catalog

Repositories

Latest version of each Zenodo concept by Logica Artificialis. A row shows only the files on that record, and a GitHub address only when the manuscript names one.

15 repositories

• 10.5281/zenodo.238320582026

  Charmenability of Thompson's group F

  Martino Lupini · Thompson groups, C*-algebras, Amenability

  We prove that Thompson's group F and its commutator subgroup F′ are charmenable. The main assertion is that every nonempty compact convex conjugation-invariant family of normalized positive-definite functions on either group contains a trace. Its proof uses commuting groups supported on disjoint intervals and a stationary averaging argument on their joint von Neumann algebra. It is independent of nonamenability of F. The character condition in charmenability follows from the classification of finite factor representations by Dudko and Medynets. We also prove that F is not charfinite and that F′ is charfinite precisely when F is nonamenable. Every nonzero simple quotient of either full group C*-algebra is scalar or is the corresponding reduced group algebra, and every nonzero nuclear quotient admits a multiplicative character.https://github.com/eulogica/charmenability-of-thompsons-group-f

  No files · GitHub named

• 10.5281/zenodo.234301632026

  Completely positive coordinates for KK-theory and relative uniform stability

  Martino Lupini · C*-algebras, Amenability, Groups

  Let A be a unital nuclear C*-algebra, M a von Neumann algebra, and I a norm-closed ideal of M. We prove that a unital completely positive map Φ:A→M, multiplicative modulo I, admits a unital homomorphic correction with the same quotient map whenever

  PDF · LaTeX · GitHub named

• 10.5281/zenodo.233625992026

  Exactness and amenability at infinity for locally compact groupoids

  Martino Lupini · Groupoids, Amenability, Groups

  For a second-countable locally compact Hausdorff étale groupoid G, we prove the equivalence of exactness of Cr*(G), exactness of reduced crossed products, and strong amenability at infinity. These conditions are also equivalent to exactness of any one twisted reduced algebra. The amenable action can be chosen with a proper open surjective anchor admitting a continuous section. This answers Anantharaman–Delaroche’s 2016 exactness questions and the étale case of LaLonde’s 2017 question about exact transformation groupoids. Consequently, exactness together with canonical weak containment implies amenability; for compact unit space, exactness is equivalent to amenability of the Furstenberg boundary action. We also prove permanence of strong amenability at infinity under continuous strongly surjective homomorphisms between second-countable groupoids with Haar systems, when the kernel and target have this property. No Haar system on the kernel is required. Finally, we construct an inner-exact étale group bundle with exact fibers and nonexact reduced algebra, supplying the example asked for by Anantharaman–Delaroche in 2016 and answering LaLonde’s 2017 group-bundle question negatively. Its fibers are hyperbolic groups converging strongly to a free group, while their Cayley graphs fail uniform property A.

  PDF · LaTeX · GitHub named

• 10.5281/zenodo.233421812026

  Bounded geometry in Polish groups: locally compact models, amenability, and simple examples

  Martino Lupini · Orderability, Descriptive set theory, Amenability

  We develop locally compact models and applications for Polish groups of bounded geometry. Building on Hrushovski's quasi-model theorem and the ultrafilter framework of Krupiński–Pillay, we give an explicit coarse-density calculation for a model with compact conjugation-invariant multiplication defect and exact control of the intrinsic coarsely bounded bornology. Applications yield the Haagerup property under topological amenability and two-sided entropy estimates under metric amenability. Packing and model obstructions treat the stated classes of groups. For McCleary's classical simple periodic coloured-order group, we compute the pointwise Polish topology and intrinsic coarse geometry, obtaining a non-locally compact quasi-line.

  PDF · LaTeX · GitHub named

• 10.5281/zenodo.233387882026

  Automatic equivariant Jiang–Su stability in the nonunital tracial setting

  Martino Lupini · C*-algebras, Amenability, Groups

  Let A be a separable simple nuclear C*-algebra that absorbs the Jiang–Su algebra Z and admits a nonzero densely defined lower semicontinuous trace. Using the Gaussian construction of the October 2026 OpenAI preprint, we prove that every action α of a countable discrete amenable group on A is cocycle conjugate to α ⊗ idZ. This answers the general tracial part of Szabó’s 2019 conjecture on automatic equivariant Jiang–Su stability, extending the October 2026 unital theorem to algebras with possibly unbounded traces and to trace-scaling actions. The extension applies that construction in a tracial quotient of Kirchberg’s central sequence algebra and uses the nonunital absorption results of Szabó and Wouters. The transfer is expressed as a local equivariant Gamma criterion for nonseparable unital algebras admitting relative copies of Z. Its uniform trace-splitting estimates allow the original action and its full cone of traces to be retained. Combined with the established purely infinite case, the result gives automatic equivariant Jiang–Su stability for all separable simple nuclear Z-stable algebras.

  PDF · LaTeX · GitHub named

• 10.5281/zenodo.228833532026

  Isomorphism of finitely generated bi-orderable elementary amenable groups is universal

  Martino Lupini · Orderability, Amenability, Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228452362026

  Skew-amenability in finite-regularity topologies for path, loop, and gauge groups

  Martino Lupini · Amenability, Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228146892026

  $\mathbf{\Sigma^0_2}$ boundaries in $\ell^1$-homology from amenable convergence actions

  Martino Lupini · Amenability

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.228133152026

  Malliavin--Malliavin and whirly amenability: Borel observations, translation displacement, and total variation

  Martino Lupini · Descriptive set theory, Amenability

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.227582302026

  Borel invariant means on countable inverse limits of amenable groups

  Martino Lupini · Descriptive set theory, Amenability, Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.227436042026

  Amenability and skew-amenability of C1 path, loop, and one-dimensional gauge groups

  Martino Lupini · Amenability, Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.227378542026

  Concentrating measures and whirly amenability of Doucha's universal metric group

  Martino Lupini · Amenability, Groups

  No abstract on this deposit.

  PDF · LaTeX

• 10.5281/zenodo.227224532026

  Extreme amenability of the automorphism group of the Jiang-Su algebra

  Martino Lupini · Amenability, Groups

  No abstract on this deposit.

  PDF · LaTeX · Data

• 10.5281/zenodo.227221902026

  Extreme amenability of the automorphism group of the Razak-Jacelon algebra

  Martino Lupini · Amenability, Groups

  No abstract on this deposit.

  LaTeX · Data

• 10.5281/zenodo.227135582026

  Extreme amenability of the additive group of $L^p$ for $0<p<1$

  Martino Lupini · Amenability, Groups

  No abstract on this deposit.

  PDF · LaTeX