Related papers: Hyperrigidity of C*-correspondences

Let (A,G) be a C*-dynamical system with G discrete. In this paper we investigate the ideal structure of the reduced crossed product C*-algebra and in particular we determine sufficient - and in some cases also necessary - conditions for A…

We develop a relative boundary theory for actions of discrete groups on compact spaces and use it to derive rigidity results for reduced crossed products. For a discrete group $\Gamma$ acting on a compact space $X$ and a subgroup $H$, we…

In the first part of the paper, we develop a theory of crossed products of a $C^*$-algebra $A$ by an arbitrary (not necessarily extendible) endomorphism $\alpha:A\to A$. We consider relative crossed products $C^*(A,\alpha;J)$ where $J$ is…

In this paper, we investigate *-homomorphisms between C*-algebras associated to \'etale groupoids. First, we prove that such a *-homomorphism can be described by closed invariant subsets, groupoid homomorphisms and cocycles under some…

Let $k$ be a field, and let $\mathcal{C}$ be a Cauchy complete $k$-linear braided category with finite dimensional morphism spaces and ${{\rm End}(\bf 1)}=k$. We call an indecomposable object $X$ of $\mathcal C$ non-negligible if there…

We investigate the hyperrigidity of subsets of unital $C^*$-algebras annihilated by states (or, more generally, by completely positive maps). This is closely related to the concept of rigidity at $0$ introduced by G. Salomon, who studied…

We prove W$^*$-superrigidity for a large class of coinduced actions. We prove that if $\Sigma$ is an amenable almost-malnormal subgroup of an infinite conjugagy class (icc) property (T) countable group $\Gamma$, the coinduced action…

We show that certain C*-algebras which have been studied among others by Arzumanian, Vershik, Deaconu, and Renault in connection to a measure preserving transformation of a measure space and/or to a covering map of a compact space are…

Arveson's hyperrigidity conjecture predicts that if the non-commutative Choquet boundary of a separable operator system $\mathcal{S}$ is the entire spectrum of its generated C*-algebra $\mathcal{B}$ then $\mathcal{S}$ is hyperrigid in…

Although Arveson's hyperrigidity conjecture was recently resolved negatively by B. Bilich and A. Dor-On, the problem remains open for commutative $C^*$-algebras. Relatively few examples of hyperrigid sets are known in the commutative case.…

Suppose that $G$ is a groupoid acting on a small category $H$ in the sense of \cite[Definition 4]{NOT} and $H\times_\alpha G$ is the resulting semi-direct product category (as in \cite[Proposition 8]{NOT}). We show that there exists a…

Let $G$ be either a profinite or a connected compact group, and $\Gamma, \Lambda$ be finitely generated dense subgroups. Assuming that the left translation action of $\Gamma$ on $G$ is strongly ergodic, we prove that any cocycle for the…

By proving that, if the quotient space S(X) of the connected components of the locally compact metric space (X,d) is compact, then the full group I(X,d) of isometries of X is closed in C(X,X) with respect to the pointwise topology, i.e.,…

We study the ideal structure of $C^*$-algebras arising from $C^*$-correspondences. We prove that gauge-invariant ideals of our $C^*$-algebras are parameterized by certain pairs of ideals of original $C^*$-algebras. We show that our…

Let X be an infinite, compact, metrizable space of finite covering dimension and h a minimal homeomorphism of X. We prove that the crossed product of C(X) by h absorbs the Jiang-Su algebra tensorially and has finite nuclear dimension. As a…

Given a C*-algebra A with a left action of a locally compact quantum group G on it and a unitary 2-cocycle Omega on \hat G, we define a deformation A_Omega of A. The construction behaves well under certain additional technical assumptions…

This is a survey article describing the proof that the crossed product C^* (Z, M, h) of a compact smooth manifold M by a minimal diffeomorphism h of M is isomorphic to a direct limit of recursive subhomogeneous C*-algebras.

We consider the following problem. Suppose $\alpha$ is an action of a locally compact group $G$ on a $C^*$-algebra $A$, $H$ is a closed subgroup of $G$, and $(\pi,U)$ is a covariant representation of $(A,H,\alpha)$. For which closed…

Given a labeling c of the edges of a directed graph E by elements of a discrete group G, one can form a skew-product graph E cross_c G. We show, using the universal properties of the various constructions involved, that there is a coaction…

We introduce and study the notion of relative rigidity for pairs $(X,\JJ)$ where 1) $X$ is a hyperbolic metric space and $\JJ$ a collection of quasiconvex sets 2) $X$ is a relatively hyperbolic group and $\JJ$ the collection of parabolics…