Related papers: Boundary maps, germs and quasi-regular representat…

We initiate a study of non-commutative Choquet boundary for spaces of unbounded operators. We define the notion of local boundary representations for local operator systems in locally C$^*$-algebras and prove that local boundary…

In this paper we consider a bootstrap class $\mathfrak C$ of countable discrete groups, which is closed under countable unions and extensions by the integers, and we study actions of such groups on C*-algebras. This class includes all…

Let $G$ be a locally compact abelian Hausdorff topological group which is non-compact and whose Pontryagin dual $\Gamma$ is partially ordered. Let $\Gamma^{+}\subset\Gamma$ be the semigroup of positive elements in $\Gamma$. The Hardy space…

We describe a special class of representations of an inverse semigroup S on Hilbert's space which we term "tight". These representations are supported on a subset of the spectrum of the idempotent semilattice of S, called the "tight…

Let $\mathcal{A}$ and $\mathcal{B}$ be two unital $C^*$-algebras and let for $C\in\mathcal{A},\ \Gamma_C=\{\gamma \in \mathbb{C} : \|C-\gamma I\|=\inf_{\alpha\in \mathbb{C}} \|C-\alpha I\|\}$. We prove that if $\Phi :\mathcal{A}…

We prove that for every exact discrete group $\Gamma$, there is an intermediate C*-algebra between the reduced group C*-algebra and the intersection of the group von Neumann algebra and the uniform Roe algebra which is realized as the…

Let $\Gamma$ be an $\widetilde A_2$ subgroup of $\PGL_3(\mathbb K)$, where $\mathbb K$ is a local field with residue field of order $q$. The module of coinvariants $C(\mathbb P^2_{\mathbb K},\mathbb Z)_{\Gamma}$ is shown to be finite, where…

We investigate a class of groups acting on possibly exotic affine buildings $X$ and possessing good proximal properties. Such groups are termed of general type, and their dynamics is analyzed through their flag limit sets in the space of…

We study the quotients of the Toeplitz C*-algebra of a quasi-lattice ordered group (G,P), which we view as crossed products by a partial actions of G on closed invariant subsets of a totally disconnected compact Hausdorff space, the Nica…

We show that the following properties of the C*-algebras in a class $\mathcal{P}$ are inherited by simple unital ${\rm C^*}$-algebras in the class of asymptotically tracially in $\mathcal{P}$: $(1)$ $\beta$-comparison (in the sense of…

We study the structure of C*-algebras associated with compactly aligned product systems over group embeddable right LCM-semigroups. Towards this end we employ controlled maps and a controlled elimination method that associates the original…

For 0 < s < 1, let phi_s(z)=sz+(1-s). We investigate the unital C*-algebra generated by the semigroup {C_{phi_s} : 0 < s < 1} of composition operators acting on the Hardy space of the unit disk. We determine the joint approximate point…

We study the automorphism group of a unital, simple, $\mathcal{Z}$-stable $C^{*}$-algebra. In this paper, we generalize the results by the authors in \cite{pr_auto} to $\mathcal{Z}$-stable $C^{*}$-algebras $\mathfrak{A}$ such that…

Let $\Gamma$ be a torsion free lattice in $G = \PGL(n+1,\FF)$, where $n\ge 1$ and $\FF$ is a non-archimedean local field. Then $\Gamma$ acts on the Furstenberg boundary $G/P$, where $P$ is a minimal parabolic subgroup of $G$. The identity…

Let E be a second-countable, locally compact, Hausdorff groupoid equipped with an action of T such that G:=E/T is a principal groupoid with Haar system \lambda. The twisted groupoid C*-algebra C*(E;G,\lambda) is a quotient of the C*-algebra…

It is shown that, given any finite dimensional, split basic algebra $\Lambda = K\Gamma/I$ (where $\Gamma$ is a quiver and $I$ an admissible ideal in the path algebra $K \Gamma$), there is a finite list of affine algebraic varieties, the…

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.…

Let A be a unital simple separable C*-algebra. If $A$ is nuclear and infinite-dimensional, it is known that strict comparison is equivalent to Z-stability if the extreme boundary of its tracial state space is non-empty, compact and of…

Exotic group $C^*$-algebras are $C^*$-algebras that lie between the universal and the reduced group $C^*$-algebra of a locally compact group. We consider simple Lie groups $G$ with real rank one and investigate their exotic group…

We study C*-algebras associated to right LCM semigroups, that is, semigroups which are left cancellative and for which any two principal right ideals are either disjoint or intersect in another principal right ideal. If $P$ is such a…