Related papers: Equivariant property (SI) revisited, II

For an action of a discrete group $\Gamma$ on a set $X$, we show that the Schreier graph on $X$ has property A if and only if the permutation representation on $\ell_2X$ generates an exact $\mathrm{C}^*$-algebra. This is well known in the…

The notion of qausi-product actions of a compact group on a C$^*$-algebra was introduced by Bratteli et al. in their attempt to seek an equivariant analogue of Glimm's characterization of non-type I C$^*$-algebras. We show that a faithful…

We define the notion of invariant derivation of a C*-algebra under a compact quantum group action and prove that in certain conditions, such derivations are generators of one parameter automorphism groups.

We give the first examples of (non-amenable group) amenable actions on stably finite simple C*-algebras. More precisely, we give such actions for any countable group in an explicit way. The main ingredients of our construction are the full…

Let $\Gamma$ be a countable group and $(X, \Gamma)$ a compact topological dynamical system. We study the question of the existence of an intermediate $C^*$-subalgebra $\mathcal{A}$ $$C^{*}_{r}(\Gamma)<\mathcal{A}<C(X)\rtimes_r\Gamma,$$…

In this note we study a natural analytic property of inclusions of groups akin to co-amenability: the property of existence of a non-compactly supported invariant state for the conjugation action of a group $G$ on the von Neumann algebra…

Suppose that $\mathcal M$ is a countably decomposable type II$_1$ von Neumann algebra and $\mathcal A$ is a separable, non-nuclear, unital C$^*$-algebra. We show that, if $\mathcal M$ has Property $\Gamma$, then the similarity degree of…

We define a notion of Property (T) for an arbitrary $C^*$-algebra $A$ admitting a tracial state. We extend this to a notion of Property (T) for the pair $(A,B),$ where $B$ is a $C^*$-subalgebra of $A.$ Let $\Gamma$ be a discrete group and…

We study the classification of group actions on C*-algebras up to equivariant KK-equivalence. We show that any group action is equivariantly KK-equivalent to an action on a simple, purely infinite C*-algebra. We show that a conjecture of…

Let $\Gamma$ be a countable group acting on a countable set $X$ by permutations. We give a necessary and sufficient condition for the action to have a quasi-invariant mean with a given cocycle. This can be viewed as a combinatorial analogue…

We prove that an action $\rho:A\to M(C_0(\mathbb{G})\otimes A)$ of a locally compact quantum group on a $C^*$-algebra has a universal equivariant compactification, and prove a number of other category-theoretic results on…

We generalize the main result of Kamalov and show that if $G$ is an amenable discrete group with an action $\alpha$ on a finite nuclear unital $C^*$-algebra $A$ such that the reduced crossed product $A\rtimes_{\alpha,r} G$ has property $T$,…

For any countable group $\Gamma$ satisfying the ``weak Rohlin property'', and for any dynamical property, the set of $\Gamma$-actions with that property is either residual or meager. The class of groups with the weak Rohlin property…

A locally compact groupoid is said to have the weak containment property if its full $C^*$-algebra coincides with its reduced one. This property is strictly weaker than amenability and is known to be equivalent to amenability for…

In this article, we generalize to the case of measured quantum groupoids on a finite basis some important results concerning actions of locally compact quantum groups on C*-algebras [S. Baaj, G. Skandalis and S. Vaes, 2003]. Let $\cal G$ be…

This paper concerns the non-commutative analog of the Normal Subgroup Theorem for certain groups. Inspired by Kalantar-Panagopoulos, we show that all $\Gamma$-invariant subalgebras of $L\Gamma$ and $C^*_r(\Gamma)$ are ($\Gamma$-)…

We generalize W*-superrigidity results about Bernoulli actions of rigid groups to general mixing Gaussian actions. We thus obtain the following: If \Gamma\ is any ICC group which is w-rigid (i.e. it contains an infinite normal subgroup with…

We introduce stabilised property Gamma, a C*-algebraic variant of property Gamma which is invariant under stable isomorphism. We then show that simple separable nuclear C*-algebras with stabilised property Gamma and $\mathrm{Cu}(A) \cong…

Amenable actions of locally compact groups on von Neumann algebras are investigated by exploiting the natural module structure of the crossed product over the Fourier algebra of the acting group. The resulting characterisation of…

By combining R{\o}rdam's construction and the author's previous construction, we provide the first examples of amenable actions of non-amenable groups on simple separable nuclear C*-algebras that are neither stably finite nor purely…