Periodic Reporting for period 2 - AMAREC (Amenability, Approximation and Reconstruction)
Période du rapport: 2021-04-01 au 2022-09-30
Amenability phenomena exist in abundance in theoretical mathematics. They provide a common viewpoint on structures and problems arising in geometry, dynamics, algebra, and functional analysis. In this project we focus on amenable (aka nuclear) C*-algebras, with a particular interest in those coming from amenable dynamical systems.
In https://arxiv.org/abs/2209.06507 Gardella, Geffen, Naryshkin, and Vaccaro establish Z-stability for crossed products of outer actions of amenable groups on Z-stable C∗-algebras under a mild technical assumption.
In https://arxiv.org/abs/2201.03409 Gardella, Geffen, Kranz, and Naryshkin show that all amenable, minimal actions of a large class of nonamenable countable groups on compact metric spaces have dynamical comparison.
In https://arxiv.org/abs/2111.15221 Lledó and Martínez show that the main C*-algebras describing the canonical commutation relations of quantum physics, i.e. the Weyl and resolvent algebras, are in the class of Følner C*-algebras.
In https://arxiv.org/abs/2107.14725 Martínez starts the study of whether the reduced C*-algebra of an inverse semigroup is quasi-diagonal.
In https://arxiv.org/abs/2108.04670 Naryshkin shows that a minimal action of a finitely generated group of polynomial growth on a compact metrizable space has comparison.
In https://arxiv.org/abs/2002.03287 Geffen bounds the nuclear dimension of crossed products associated to some partial actions of finite groups or ℤ on finite dimensional locally compact Hausdorff second countable spaces.
In https://arxiv.org/abs/2012.03650 Evington obtains an improved upper bound for the nuclear dimension of extensions of O_\infty-stable C^*-algebras.
In https://arxiv.org/abs/2105.05587 Evington and Girón Pacheco study the H^3 invariant of a group homomorphism ϕ:G→Out(A), where A is a classifiable C^*-algebra.
In https://arxiv.org/abs/2101.08556 Armstrong, de Castro, Orloff Clark, Courtney, Lin, McCormick, Ramagge, Sims, and Steinberg show how to recover a discrete twist over an ample Hausdorff groupoid from a pair consisting of an algebra and what they call a quasi-Cartan subalgebra.