Related papers: Graph inverse semigroups, groupoids and their C*-a…

Quantum symmetry of a graph $C^{*}$-algebra $C^{*}(\Gamma)$ corresponding to a finite graph $\Gamma$ has been explored by several mathematicians within different categories in the past few years. In this article, we establish that there are…

The study of graph C*-algebras has a long history in operator algebras. Surprisingly, their quantum symmetries have never been computed so far. We close this gap by proving that the quantum automorphism group of a finite, directed graph…

In the standard category of directed graphs, graph morphisms map edges to edges. By allowing graph morphisms to map edges to finite paths (path homomorphisms of graphs), we obtain an ambient category in which we determine subcategories…

We describe a construction by G\'abor Elek, associating C*-algebras with uniformly recurrent subgroups, in the language of groupoid C*-algebras. This allows us to simplify several proofs in the original paper and fully characterise their…

Given a graph $E$, an action of a group $G$ on $E$, and a $G$-valued cocycle $\phi$ on the edges of $E$, we define a C*-algebra denoted ${\cal O}_{G,E}$, which is shown to be isomorphic to the tight C*-algebra associated to a certain…

This research notes is intended to provide a quick introduction to the subject. We expose a K-theoretic approach to study group C*-algebras: started in the elementary part, with one example of description of the structure of C*-algebras of…

Let $G$ be a Hausdorff, \'etale groupoid that is minimal and topologically principal. We show that $C^*_r(G)$ is purely infinite simple if and only if all the nonzero positive elements of $C_0(G^0)$ are infinite in $C_r^*(G)$. If $G$ is a…

We prove that the C*-algebra of a second-countable, \'etale, amenable groupoid is simple if and only if the groupoid is topologically principal and minimal. We also show that if G has totally disconnected unit space, then the associated…

We construct uncountably many mutually nonisomorphic simple separable stably finite unital exact C$^\ast$-algebras which are not isomorphic to their opposite algebras. In particular, we prove that there are uncountably many possibilities…

Semigroup C*-algebras for right-angled Artin monoids were introduced and studied by Crisp and Laca. In the paper at hand, we are able to present the complete answer to their question of when such C*-algebras are isomorphic. The answer to…

We give an alternative construction of the essential $C^*$-algebra of an \'etale groupoid, along with an ``amenability'' notion for such groupoids that is implied by the nuclearity of this essential $C^*$-algebra. In order to do this we…

I introduce yet another way to associate a C*-algebra to a graph and construct a simple nuclear C*-algebra that has irreducible representations both on a separable and a nonseparable Hilbert space.

We classify graph C*-algebras, namely, Cuntz-Krieger algebras associated to the Bass-Hashimoto edge incidence operator of a finite graph. This is done by a purely graph theoretical calculation of the K-theory and the position of the unit…

A simple Steinberg algebra associated to an ample Hausdorff groupoid $G$ is algebraically purely infinite if and only if the characteristic functions of compact open subsets of the unit space are infinite idempotents. If a simple Steinberg…

We define an admissible decomposition of a graph $E$ into subgraphs $F_1$ and $F_2$, and consider the intersection graph $F_1\cap F_2$ as a subgraph of both $F_1$ and $F_2$. We prove that, if the graph $E$ is row finite and its…

We find a substantial class of pairs of $*$-homomorphisms between graph C*-algebras of the form $C^*(E)\hookrightarrow C^*(G)\twoheadleftarrow C^*(F)$ whose pullback C*-algebra is an AF graph C*-algebra. Our result can be interpreted as a…

We investigate the ideal structures of the C^*-algebras arising from topological graphs. We give the complete description of ideals of such C^*-algebras which are invariant under the so-called gauge action, and give the condition on…

We consider infinite connected quasi-transitive locally finite graphs and show that every such graph with more than one end is a tree amalgamation of two other such graphs. This can be seen as a graph-theoretical version of Stallings'…

Using the Baum-Connes conjecture with coefficients, we develop a K-theory formula for reduced C*-algebras of strongly $0$-$E$-unitary inverse semigroups, or equivalently, for certain reduced partial crossed products. In the case of…

We describe the $C^*$-algebra of an $E$-unitary or strongly 0-$E$-unitary inverse semigroup as the partial crossed product of a commutative $C^*$-algebra by the maximal group image of the inverse semigroup. We give a similar result for the…