Related papers: Nuclearity and Exactness for Groupoid Crossed Prod…

In this paper, we give a complete, two-way characterization, of when a noncommutative crossed product $A \rtimes_\lambda G$ is simple, in the case of $G$ being an FC-hypercentral group. This is a large class of amenable groups that contains…

A discrete group $\Gamma$ is called exact if the reduced group C*-algebra ${C_{\lambda}}^{*}(\Gamma)$ is exact as C*-algebras, and a discrete group $\Lambda$ is called residually exact if every nonunital element $g \in \Lambda$ admits a…

We generalize a theorem of Chifan and Ioana by proving that for any, possibly type III, amenable von Neumann algebra $A_0$, any faithful normal state $\varphi_0$ and any discrete group $\Gamma$, the associated Bernoulli crossed product von…

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…

If $\alpha$ is an amenable action of a discrete group $G$ on a unital C*-algebra $A$, then the crossed-product C*-algebra $A\rtimes_\alpha G$ has the weak expectation property if and only if $A$ has this property.

We consider the tracial crossed product algebra $M=A\rtimes\Lambda$ arising from a trace preserving action $\sigma:\Lambda \curvearrowright A$ of a discrete group $\Lambda$ on a tracial von Neumann algebra $A$. For a unitary subgroup…

We construct explicit approximating nets for crossed products of C*-algebras by actions of discrete quantum groups. This implies that C*-algebraic approximation properties such as nuclearity, exactness or completely bounded approximation…

In 1990, Rieffel defined a notion of proper action of a group $H$ on a $C^*$-algebra $A$. He then defined a generalized fixed point algebra $A^{\alpha}$ for this action and showed that $A^{\alpha}$ is Morita equivalent to an ideal of the…

Let $\Gamma^{+}$ be the positive cone of a totally ordered abelian discrete group $\Gamma$, and $\alpha$ an action of $\Gamma^{+}$ by extendible endomorphisms of a $C^*$-algebra $A$. We prove that the partial-isometric crossed product…

For Ore semigroups $P$ with an order unit, we prove that there is a bijection between $E_0$-semigroups over $P$ and product systems of $C^{*}$-correspondences over $P^{op}$. We exploit this bijection and show that the reduced…

We examine the ideal structure of crossed products B\rtimes G where B is a continuous-trace C*-algebra and the induced action of G on the spectrum of B is proper. In particular, we are able to obtain a concrete description of the topology…

Consider a projective limit G of finite groups G_n. Fix a compatible family \delta^n of coactions of the G_n on a C*-algebra A. From this data we obtain a coaction \delta of G on A. We show that the coaction crossed product of A by \delta…

Our purpose is to study in the setting of locally compact groupoids the analogues of the well-known equivalent definitions of exactness for discrete groups. Our best results are obtained for a class of \'etale groupoids that we call inner…

Let $A$ be an infinite-dimensional stably finite simple unital C*-algebra, let $G$ be a finite group, and let $\alpha\colon G\rightarrow \mathrm{Aut}(A)$ be an action of $G$ on $A$ which has the weak tracial Rokhlin property. We prove that…

Suppose that $G$ has a representation group $H$, that $G_{ab}:= G/\bar{[G,G]}$ is compactly generated, and that $A$ is a \cs-algebra for which the complete regularization of $\Prim(A)$ is a locally compact Hausdorff space $X$. In a previous…

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 in the uniform trace norm. We characterize tracial…

A subgroup of an amenable group is amenable. The $C^*$-algebra version of this fact is false. This was first proved by M.-D. Choi who proved that the non-nuclear $C^*$-algebra $C^*_r(\ZZ_2*\ZZ_3)$ is a subalgebra of the nuclear Cuntz…

It is shown that if A is an AF algebra then a crossed product of A by the integers can be embedded into an AF algebra if and only if the crossed product is stably finite. This equivalence follows from a simple K-theoretic characterization…

We introduce the notion of a $\mathbb{G}$-operator space $(X, \alpha)$, which consists of an action $\alpha: X \curvearrowleft \mathbb{G}$ of a locally compact quantum group $\mathbb{G}$ on an operator space $X$, and we make a study of the…

Let (A,G,\alpha) be a partial dynamical system. We show that there is a bijective correspondence between G-invariant ideals of A and ideals in the partial crossed product A xr G provided the action is exact and residually topologically…