Tracially amenable actions and purely infinite crossed products

E Gardella, S Geffen, J Kranz, P Naryshkin… - Mathematische …, 2024 - Springer
We introduce the notion of tracial amenability for actions of discrete groups on unital, tracial
C∗-algebras, as a weakening of amenability where all the relevant approximations are done …

Equivariant property (SI) revisited, II

G Szabó - arXiv preprint arXiv:2308.08878, 2023 - arxiv.org
We investigate Matui-Sato's notion of property (SI) for C*-dynamics, this time with a focus on
actions of possibly non-amenable groups. The main result is a generalization of earlier work …

Amenable actions on finite simple C*-algebras arising from flows on Pimsner algebras

Y Suzuki - arXiv preprint arXiv:2305.13056, 2023 - arxiv.org
Associated to a family of $ G $-$\ast $-endomorphisms on a $ G $-C*-algebra $ A $
satisfying certain minimality conditions, we give a $ G $-C*-correspondence $\mathcal {E} …

Actions on classifiable C*‐algebras without equivariant property (SI)

E Gardella, J Kranz, A Vaccaro - Bulletin of the London …, 2024 - Wiley Online Library
We exhibit examples of actions of countable discrete groups on both simple and non‐simple
nuclear stably finite C*‐algebras that are tracially amenable but not amenable. We …

Amenable actions on ill-behaved simple C*-algebras

Y Suzuki - arXiv preprint arXiv:2405.10191, 2024 - arxiv.org
By combining R {\o} rdam's construction and author's previous construction, we provide the
first examples of amenable actions on simple separable nuclear C*-algebras that are neither …

Continuous actions on primitive ideal spaces lift to C* C^∗‐actions

M Pagliero - Bulletin of the London Mathematical Society, 2024 - Wiley Online Library
We prove that for any second‐countable, locally compact group GG, any continuous GG‐
action on the primitive ideal space of a separable, nuclear C* C^∗‐algebra BB such that B≅ …