Related papers: Nuclearity of Hypergraph C*-Algebras

We prove that the pure state space is homogeneous under the action of the automorphism group (or a certain smaller group of approximately inner automorphisms) for a fairly large class of simple separable nuclear C*-algebras, including the…

The class of simple separable KK-contractible (KK-equivalent to $\{0\}$) C*-algebras which have finite nuclear dimension is shown to classified by the Elliott invariant. In particular, the class of C*-algebras $A\otimes \mathcal W$ is…

We introduce a family of $C^*$-correspondences $X_\alpha$ naturally associated to every ordinal graph $\Lambda$. When $\Lambda$ is a directed graph, $X_0$ is isomorphic to the usual $C^*$-correspondence associated to a graph. We show that…

The notion of a self-similar ultragraph $(G,\mathcal{U},\varphi)$ and its $C^*$-algebra $\mathcal{O}_{G,\mathcal{U}}$ were introduced in our recent work, where we proposed inverse semigroup and groupoid models for such $C^*$-algebras as…

It has been a longstanding problem whether every amenable operator algebra is isomorphic to a (necessarily nuclear) C*-algebra. In this note, we give a nonseparable counterexample. The existence of a separable counterexample remains an open…

The subject of quasidiagonality is of much interest in many places - among other things, in the classification program for simple unital separable nuclear C*-algebras. In this note, we give two characterizations of nuclearity and…

Quantum symmetry of graph $C^{*}$-algebras has been studied, under the consideration of different formulations, in the past few years. It is already known that the compact quantum group $(\underbrace{C(S^{1})*C(S^{1})*\cdots…

We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…

In this note we generalize a result from a recent paper of Hajac, Reznikoff and Tobolski (2020). In that paper they give conditions they call admissibility on a pushout diagram in the category of directed graphs implying that the…

This dissertation concerns the classification of groupoid and higher-rank graph C*-algebras and has two main components. Firstly, for a groupoid it is shown that the notions of strength of convergence in the orbit space and…

We prove a uniqueness theorem and give a characterization of simplicity for Steinberg algebras associated to non-Hausdorff ample groupoids. We also prove a uniqueness theorem and give a characterization of simplicity for the C*-algebra…

We analyse a notion of $C^*$-independence for $\mathbb{Z}_2$-graded $C^*$-algebras. We provide other notions of statistical independence for $\mathbb{Z}_2$-graded von Neumann algebras and prove some relationships between them. We provide a…

A triangular limit algebra A is isometrically isomorphic to the tensor algebra of a C*-correspondence if and only if its fundamental relation R(A) is a tree admitting a $Z^+_0$-valued continuous and coherent cocycle. For triangular limit…

A partial action is associated with a normal weakly left resolving labelled space such that the crossed product and labelled space $C^*$-algebras are isomorphic. An improved characterization of simplicity for labelled space $C^*$-algebras…

The class of simple separable KK-contractible (KK-equivalent to $\{0\}$) C*-algebras which have finite nuclear dimension is shown to be classified by the Elliott invariant. In particular, the class of C*-algebras $A\otimes \mathcal W$ is…

We systematically investigate $C^*$-norms on the algebraic graded product of $\mathbb{Z}_2$-graded $C^*$-algebras. This requires to single out the notion of a compatible norm, that is a norm with respect to which the product grading is…

In the given article it is introduced new notions of a C$^*$-algebra of von Neumann type I and C$^*$-algebras of types I$_n$, II, II$_1$, II$_\infty$ and III. It is proved that any GCR-algebra is a C$^*$-algebra of von Neumann type I, and a…

In this paper we study the nuclearity and weak containment property of reduced cross-sectional C*-algebras of Fell bundles over inverse semigroups. In order to develop the theory, we first prove an analogue of Fell's absorption trick in the…

In this paper we explore a generic notion of superrigidity for von Neumann algebras $L(G)$ and reduced $C^*$-algebras $C^*_r(G)$ associated with countable discrete groups $G$. This allows us to classify these algebras for various new…

In this paper we suggest a definition for a C*-algebra attached to an injective morphism of some \'Etale groupoid. We take into account all the peculiarities of such objects and present some interesting relations with already well-known…