相关论文: Rohlin properties for $Z^d$-actions on the Cantor …

We prove several results of the following general form: automorphisms of (or actions of ${\mathbb{Z}}^d$ on) certain kinds of simple separable unital C*-algebras $A$ which have a suitable version of the Rokhlin property are generic among…

We establish four results concerning connections between actions on separable C*-algebras with Rokhlin-type properties and absorption of the Jiang-Su algebra Z. For actions of residually finite groups or of the reals which have finite…

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…

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…

Let A be a unital separable C*-algebra, and D a K_1-injective strongly self-absorbing C*-algebra. We show that if A is D-absorbing, then the crossed product of A by a compact second countable group or by Z or by R is D-absorbing as well,…

In this paper we study conditions under which a free minimal $\mz^d$-action on the Cantor set is a topological extension of the action of $d$ rotations, either on the product $\mt^d$ of $d$ 1-tori or on a single 1-torus $\mt^1$. We extend…

We show that group actions on many treelike compact spaces are not too complicated dynamically. We first observe that an old argument of Seidler implies that every action of a topological group $G$ on a regular continuum is null and…

We study Z-actions on unital simple separable stably finite C*-algebras of finite nuclear dimension. Assuming that the extreme boundary of the trace space is compact and finite dimensional, and that the induced action on the trace space is…

We consider Z-actions (single automorphisms) on a unital simple AH algebra with real rank zero and slow dimension growth and show that the uniform outerness implies the Rohlin property under some technical assumptions. Moreover, two…

A countable group $G$ has the strong topological Rokhlin property (STRP) if it admits a continuous action on the Cantor space with a comeager conjugacy class. We show that having the STRP is a symbolic dynamical property. We prove that a…

We will show a centrally free action of an amenable rigid C$^*$-tensor category on a properly infinite von Neumann algebra has the Rohlin property. This enables us to prove the fullness of the crossed product of a full factor by minimal…

We define a Rohlin property for actions of $Z^{2}$ on UHF algebras and show a noncommutative Rohlin type theorem. Among those actions with the Rohlin property, we classify product type actions up to outer conjugacy. In particular we present…

We consider lattice field theories with topological actions, which are invariant against small deformations of the fields. Some of these actions have infinite barriers separating different topological sectors. Topological actions do not…

We build on work of Elek and Zucker and develop a topological analogue of the theory of weak containment. We show that definitions in terms of local patterns, containment in ultra(co)products, and continuous model theory are all equivalent,…

We consider isometric actions of lattices in semisimple algebraic groups on (possibly non-compact) homogeneous spaces with (possibly infinite) invariant Radon measure. We assume that the action has a dense orbit, and demonstrate two novel…

We study compact group actions with finite Rokhlin dimension, particularly in relation to crossed products. For example, we characterize the duals of such actions, generalizing previous partial results for the Rokhlin property. As an…

Group actions on a Smale space and the actions induced on the C*-algebras associated to such a dynamical system are studied. We show that an effective action of a discrete group on a mixing Smale space produces a strongly outer action on…

We give examples of actions of Z/2Z on AF algebras and AT algebras which demonstrate the differences between the (strict) Rokhlin property and the tracial Rokhlin property, and between (strict) approximate representability and tracial…

Given a countable group $G$, we initiate a systematic study of the Polish spaces of all minimal and topologically transitive actions of $G$ on the Cantor space by homeomorphisms, with a focus on the existence of comeager conjugacy classes…

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…