Related papers: A Cuntz-Krieger Uniqueness Theorem for Cuntz-Pimsn…

We prove that if \Lambda is a row-finite k-graph with no sources, then the associated C^*-algebra is simple if and only if \Lambda is cofinal and satisfies Kumjian and Pask's Condition (A). We prove that Condition (A) is equivalent to a…

Topological quivers generalize the notion of directed graphs in which the sets of vertices and edges are locally compact (second countable) Hausdorff spaces. Associated to a topological quiver $Q$ is a $C^*$-correspondence, and in turn, a…

By using C*-correspondences and Cuntz-Pimsner algebras, we associate to every subshift (also called a shift space) $X$ a C*-algebra $O_X$, which is a generalization of the Cuntz-Krieger algebras. We show that $O_X$ is the universal…

We study the problem of determining when the reduced twisted group C*-algebra associated with a discrete group G is simple and/or has a unique tracial state, and present new sufficient conditions for this to hold. One of our main tools is a…

We show that if $G$ is a second countable locally compact Hausdorff \'etale groupoid carrying a suitable cocycle $c:G\to\mathbb{Z}$, then the reduced $C^*$-algebra of $G$ can be realised naturally as the Cuntz-Pimsner algebra of a…

In this paper we generalize the notion of Cuntz-Pimsner algebras of $C^*$-correspondences to the setting of subproduct systems. The construction is justified in several ways, including the Morita equivalence of the operator algebras under…

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 consider the higher-rank graphs introduced by Kumjian and Pask as models for higher-rank Cuntz-Krieger algebras. We describe a variant of the Cuntz-Krieger relations which applies to graphs with sources, and describe a local convexity…

Given a quantum graph $\mathcal{G}=(B,\psi,A)$, we define a C*-correspondence $E_\mathcal{G}$ over the noncommutative vertex C*-algebra $B$, called the quantum edge correspondence. For a classical graph $\mathcal{G}$, $E_\mathcal{G}$ is the…

We describe a method of adding tails to C*-correspondences which generalizes the process used in the study of graph C*-algebras. We show how this technique can be used to extend results for augmented Cuntz-Pimsner algebras to C*-algebras…

We introduce the notion of a self-similar action of a groupoid $G$ on a finite higher-rank graph. To these actions we associate a compactly aligned product system of Hilbert bimodules, and thereby obtain corresponding universal…

We show that if $A$ is a unital $C^*$-algebra and $B$ is a Cuntz-Krieger algebra for which $A\otimes\mathbb{K} \cong B\otimes\mathbb{K}$, then $A$ is a Cuntz-Krieger algebra. Consequently, corners of Cuntz-Krieger algebras are Cuntz-Krieger…

We introduce a divisibility-type condition for directed graphs that is necessary for $\mathcal{Z}$-stability of the corresponding graph $C^*$-algebra. We prove that this condition is sufficient if either the graph $E$ has no cycles or the…

We give a notion of quantum automorphism group of graph C*-algebras without sink at critical inverse temperature. This is defined to be the universal object of a category of CQG's having a linear action in the sense of [11] and preserving…

In this paper we describe a new method of defining C*-algebras from oriented combinatorial data, thereby generalizing the constructions of algebras from directed graphs, higher-rank graphs, and ordered groups. We show that only the most…

We continue the study of $L^p$-operator algebras associated with directed graphs initiated by Corti\~nas and Rodr\'iguez, and we establish $L^p$-analogs of both the gauge-invariant and the Cuntz-Krieger uniqueness theorems. The first of…

Given an arbitrary countable directed graph $G$ we prove the C*-envelope of the tensor algebra $T_+(G)$ coincides with the universal Cuntz-Krieger algebra associated with $G$. Our approach is concrete in nature and does not rely on Hilbert…

Cuntz algebra $\mathcal O_2$ is the universal $C^*$-algebra generated by two isometries $s_1, s_2$ satisfying $s_1s_1^*+s_2s_2^*=1$. This is separable, simple, infinite $C^*$-algebra containing a copy of any nuclear $C^*$-algebra. The…

To every $C^*$ correspondence over a $C^*$-algebra one can associate a Cuntz-Pimsner algebra generalizing crossed product constructions, graph $C^*$-algebras, and a host of other classes of operator algebras. Cuntz-Pimsner algebras come…

We extend the the definition of Kumjian-Pask algebras to include algebras associated to finitely aligned higher-rank graphs. We show that these Kumjian-Pask algebras are universally defined and have a graded uniqueness theorem. We also…