相关论文: Residually finite actions and crossed products

In this note, we consider the concentration function problem for a continuous action of a locally compact group $G$ on a locally compact Hausdorff space $X$. We prove a necessary and sufficient condition for the concentration functions of a…

We study conditions that will ensure that a crossed product of a C*-algebra by a discrete exact group is purely infinite (simple or non-simple). We are particularly interested in the case of a discrete non-amenable exact group acting on a…

We introduce and study the notions of boundary actions and of the Furstenberg boundary of a discrete quantum group. As for classical groups, properties of boundary actions turn out to encode significant properties of the operator algebras…

We expand the class of groups with relatively geometric actions on CAT(0) cube complexes by proving that it is closed under $C'(\frac16)$--small cancellation free products. We build upon a result of Martin and Steenbock who prove an…

We study the space of ends of groups. For a finitely generated group, this is a Cantor space as soon as it is infinite. In contrast, we show that for infinitely generated countable groups, it exhibits several behaviors. For instance, we…

In this article, we consider products of random walks on finite groups with moderate growth and discuss their cutoffs in the total variation. Based on several comparison techniques, we are able to identify the total variation cutoff of…

We show every isometric action is quasidiagonal in a strong sense. This shows that reduced crossed products by such actions are quasidiagonal or MF whenever the reduced algebra of the acting group is quasidiagonal or MF.

We generalize the notion of isoperimetric profiles of finitely generated groups to their actions by measuring the boundary of finite subgraphings of the orbit graphing. We prove that like the classical isoperimetric profiles for groups,…

For $p \in [1, \infty),$ we define and study full and reduced crossed products of algebras of operators on $\sigma$-finite $L^p$ spaces by isometric actions of second countable locally compact groups. We give universal properties for both…

In this paper, we study the deformation of the intersection of one compact set with a closed neighborhood of another compact set by changing the radius of this neighborhood. It is shown that in finite-dimensional normed spaces, in the case…

In this paper we discuss connections between the following properties: (RFM) residual finiteness of a monoid M; (RFSG) residual finiteness of Schutzenberger groups of M; and (RFRL) residual finiteness of the natural actions of M on its…

In this paper we consider the finite groups that act fiber- and orientation-preservingly on closed, compact, and orientable Seifert manifolds that fiber over an orientable base space. We establish a method of constructing such group actions…

Let C be a class of groups. We give sufficient conditions ensuring that a free product of residually C groups is again residually C, and analogous conditions are given for locally embeddable into C groups. As a corollary, we obtain that the…

A compactly generated group is noncompact if and only if it admits a nonconstant harmonic function (for some, equivalently for every, reasonable measure). This generalizes the known fact that a finitely generated group is infinite if and…

In this article we produce an example of a non-residually finite group which admits a uniformly proper action on a Gromov hyperbolic space.

Let $\alpha : \Gamma \curvearrowright A$ be an action of a discrete group $\Gamma$ on a unital C*-algebra $A$ by *-automorphisms and let $A \rtimes_{\alpha,\lambda} \Gamma$ denote the corresponding reduced crossed product C*-algebra.…

We describe the structure of the irreducible representations of crossed products of unital C*-algebras by actions of finite groups in terms of irreducible representations of the C*-algebras on which the groups act. We then apply this…

A homomorphism from a completely metrizable topological group into a free product of groups whose image is not contained in a factor of the free product is shown to be continuous with respect to the discrete topology on the range. In…

We show that the dynamic asymptotic dimension of a minimal free action of an infinite virtually cyclic group on a compact Hausdorff space is always one. This extends a well-known result of Guentner, Willett, and Yu for minimal free actions…

For an action $\alpha$ of a locally compact group $G$ on a dual operator space $X$ by w*-continuous completely isometric isomorphisms one can define two generally different notions of crossed products, namely the Fubini crossed product…