相关论文: Residually finite actions and crossed products

We show that any graph product of residually finite monoids is residually finite. As a special case we obtain that any free product of residually finite monoids is residually finite. The corresponding results for graph products of…

Let $G$ be the generalized free product of two groups with an amalgamated subgroup. We propose an approach that allows one to use results on the residual $p$-finiteness of $G$ for proving that this generalized free product is residually a…

It is shown that a locally compact second countable group $G$ has the Haagerup property if and only if there exists a sharply weak mixing 0-type measure preserving free $G$-action $T=(T_g)_{g\in G}$ on an infinite $\sigma$-finite standard…

Let a group $G$ act properly discontinuously and cocompactly on a locally compact space $X$. A Hausdorff compact space $Z$ that contains $X$ as an open subspace has the perspectivity property if the action $G\curvearrowright X$ extends to…

We consider large finite group-actions on surfaces and discuss and compare various notions for such actions: Hurwitz actions and Hurwitz groups; maximal reducible and completely reducible actions; bounding and geometrically bounding…

Let $\alpha: G\curvearrowright X$ be a minimal free continuous action of an infinite countable amenable group on an infinite compact metrizable space. In this paper, under the hypothesis that the invariant ergodic probability Borel measure…

We consider group actions of topological groups on C*-algebras of the types which occur in many physics models. These are singular actions in the sense that they need not be strongly continuous, or the group need not be locally compact. We…

We provide a sufficient condition for a topological partial action of a Hausdorff group on a metric space is continuous, provide that it is separately continuous.

We characterize supramenable groups in terms of existence of invariant probability measures for partial actions on compact Hausdorff spaces and existence of tracial states on partial crossed products. These characterizations show that, in…

Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work [2] residual finiteness of quandles was introduced, and it was proved that free…

We study certain actions of finitely generated abelian groups on higher dimensional noncommutative tori. Given a dimension $d$ and a finitely generated abelian group $G$, we apply a certain function to detect whether there is a simple…

We introduce a natural pseudometric on the space of actions of d-generated groups. In this pseudometric, the zero classes correspond to the weak equivalence classes defined by Kechris, and the metric identification is compact. We achieve…

An action of a group $G$ on a set $X$ is called ``decent'' if every subgroup of $G$ with a finite orbit in $X$ fixes a point in $X$ and every finitely generated subgroup of $G$ such that every element of the subgroup fixes a point of $X$…

We survey the results required to pass between full and reduced coactions of locally compact groups on C*-algebras, which say, roughly speaking, that one can always do so without changing the crossed-product C*-algebra. Wherever possible we…

We prove the first rigidity and classification theorems for crossed product von Neumann algebras given by actions of non-discrete, locally compact groups. We prove that for arbitrary free probability measure preserving actions of connected…

We define spectral freeness for actions of discrete groups on C*-algebras. We relate spectral freeness to other freeness conditions; an example result is that for an action of a finite group, spectral freeness is equivalent to strong…

We show that a minimal action of a finitely generated group of polynomial growth on a compact metrizable space has comparison. It follows that if such an action has the small boundary property then it is almost finite and its $C^*$-crossed…

We give a survey of recent classification results for crossed product von Neumann algebras arising from measure preserving group actions on probability spaces. This includes II_1 factors with uncountable fundamental groups and the…

We show that every finitely-generated non-amenable linear group over a field of characteristic zero admits an ergodic action which is rigid in the sense of Popa. If this group has trivial solvable radical, we prove that these actions can be…

Let $G$ be a finite group, $A$ a unital separable finite simple nuclear C*-algebra, and $\alpha$ an action of $G$ on $A$. Assume that $A$ absorbs the Jiang-Su algebra $\mathcal{Z}$, the extremal boundary of the trace space of $A$ is compact…