Related papers: Applications of model theory to C*-dynamics

Let $G$ be a metrizable compact group, $A$ a separable C*-algebra and $\alpha$ a strongly continuous action of $G$ on $A$. Provided that $\alpha$ satisfies the continuous Rokhlin property, we show that the property of satisfying the UCT in…

We study circle actions with the Rokhlin property, in relation to their restrictions to finite subgroups. We construct examples showing the following: the restriction of a circle action with the Rokhlin property (even on a real rank zero…

We show that any finite group admits actions on simple AF algebras with unique trace which have arbitrarily large finite values of Rokhlin dimension with commuting towers. We show similar results for actions of compact Lie groups, with AH…

We investigate symmetries on unital Kirchberg algebras with respect to the Rokhlin property and finite Rokhlin dimension. In stark contrast to the restrictiveness of the Rokhlin property, every such outer action has Rokhlin dimension at…

We define and examine sequentially split $*$-homomorphisms between $\mathrm{C}^*$-algebras and $\mathrm{C}^*$-dynamical systems. For a $*$-homomorphism, the property of being sequentially split can be regarded as an approximate weakening of…

We investigate the structure of circle actions with the Rokhlin property, particularly in relation to equivariant $KK$-theory. Our main results are $\mathbb{T}$-equivariant versions of celebrated results of Kirchberg: any Rokhlin action on…

Let $P \subset A$ be an inclusion of $\sigma$-unital C*-algebras with a finite index in the sense of Izumi. Then we introduce the Rokhlin property for a conditional expectation $E$ from $A$ onto $P$ and show that if $A$ is simple and…

We introduce and study a Rokhlin-type property for actions of finite groups on (not necessarily unital) C*-algebras. We show that the corresponding crossed product C*-algebras can be locally approximated by C*-algebras that are stably…

We study Rokhlin dimension of Z^m-actions on simple separable stably finite nuclear C*-algebras. We prove that under suitable assumptions, a strongly outer Z^m-action has finite Rokhlin dimension. This extends the known result for…

We introduce the spatial Rokhlin property for actions of coexact compact quantum groups on $\mathrm{C}^*$-algebras, generalizing the Rokhlin property for both actions of classical compact groups and finite quantum groups. Two key…

We introduce and systematically study the notion of Rokhlin dimension (with and without commuting towers) for compact group actions on $C^*$-algebras. This notion generalizes the one introduced by Hirshberg, Winter and Zacharias for finite…

We discuss a strategy for classifying anomalous actions through model action absorption. We use this to upgrade existing classification results for Rokhlin actions of finite groups on C$^*$-algebras, with further assuming a UHF-absorption…

In this paper we will introduce the tracial Rokhlin property for an inclusion of separable simple unital C*-algebras $P \subset A$ with finite index in the sense of Watatani, and prove theorems of the following type. Suppose that $A$…

In a previous paper, we introduced the restricted tracial Rokhlin property with comparison, a ``tracial'' analog of the Rokhlin property for actions of second countable compact groups on infinite dimensional simple separable unital…

In this paper we define a Rokhlin property for automorphisms of non-unital C*-algebras and for endomorphisms. We show that the crossed product of a C*-algebra by a Rokhlin automorphism preserves absorption of a strongly self-absorbing…

We define a "tracial" analog of the Rokhlin property for actions of second countable compact groups on infinite dimensional simple separable unital C*-algebras. We prove that fixed point algebras under such actions (and, in the appropriate…

We define "tracial" analogs of the Rokhlin property for actions of finite groups, approximate representability of actions of finite abelian groups, and of approximate innerness. We prove four analogs of related "nontracial" results. First,…

In the current article, we prove the cross product $C^*$-algebra by a Rokhlin action of finite group on a strongly quasidiagonal $C^*$-algbra is strongly quasidiagonal again. We also show that a just-infinite $C^*$-algebra is quasidiagonal…

We prove that a number of classes of separable unital C*-algebras are closed under crossed products by finite group actions with the Rokhlin property, including: (1) AI algebras, AT algebras, and related classes characterized by direct…

We extend the notion of Rokhlin dimension from topological dynamical systems to $C^*$-correspondences. We show that in the presence of finite Rokhlin dimension and a mild quasidiagonal-like condition (which, for example, is automatic for…