Related papers: Characterizing Liminal And Type I Graph C*-Algebra…

We consider *-linear maps into a commutative C*-algebra C (X) of continuous functions on a locally compact Hausdorff space X with certain specified properties and prove two results: (1) an extension result for a class of *-linear maps Y -->…

Any unital separable continuous C(X)-algebra with properly infinite fibres is properly infinite as soon as the compact Hausdorff space X has finite topological dimension. We study conditions under which this is still the case in the…

In this paper we further develop the theory of one sided shift spaces over infinite alphabets, characterizing one-step shifts as edge shifts of ultragraphs and partially answering a conjecture regarding shifts of finite type (we show that…

We define a notion of (one-sided) edge shift spaces associated to ultragraphs. In the finite case our notion coincides with the edge shift space of a graph. In general, we show that our space is metrizable and has a countable basis of…

A classification is given of certain separable nuclear C*-algebras not necessarily of real rank zero, namely, the class of separable simple C*-algebras which are inductive limits of continuous-trace C*-algebras whose building blocks have…

We use a characterization of the graph C*-algebras C*(E) as the Stacey crossed product C*(E)^\gamma \times_{\beta_E} N, to study its ideal properties in terms of the (non-classical) C*-dynamical system (C*(E)^\gamma, \beta_E)

We give a complete $K$-theoretical description of when an extension of two simple graph $C^{*}$-algebras is again a graph $C^{*}$-algebra.

We write arbitrary separable nuclear C*-algebras as limits of inductive systems of finite-dimensional C*-algebras with completely positive connecting maps. The characteristic feature of such CPC*-systems is that the maps become more and…

We introduce the concept of a 1-coaligned $k$-graph and prove that the shift maps of a $k$-graph pairwise *-commute if and only if the $k$-graph is 1-coaligned. We then prove that for 2-graphs $\Lambda$ generated from basic data *-commuting…

We describe simplicity of the Stacey crossed product A\times_\beta \N in terms of conditions of the endomorphism \beta. Then, we use a characterization of the graph C*-algebras C*(E) as the Stacey crossed product…

We survey various aspects of infinite extremal graph theory and prove several new results. The lead role play the parameters connectivity and degree. This includes the end degree. Many open problems are suggested.

Let C be a finite connected graph for which there is a countable universal C-free graph, and whose tree of blocks is a path. Then the blocks of C are complete. This generalizes a result of Furedi and Komjath, and fits naturally into a set…

We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense.…

For a finitely aligned k-graph $\Lambda$ with X a set of vertices in $\Lambda$ we define a universal C*-algebra called $C^*(\Lambda,X)$ generated by partial isometries. We show that $C^*(\Lambda,X)$ is isomorphic to the corner…

The codegree of an irreducible character $\chi$ of a finite group $G$ is defined as $|G:\ker\chi|/\chi(1)$. The codegree graph $\Gamma(G)$ of a finite group $G$ is the graph whose vertices are the prime divisors of $|G|$, where two distinct…

Motivated by the study of traces on graph $C^*$-algebras, we consider traces (additive, central maps) on Leavitt path algebras, the algebraic counterparts of graph $C^*$-algebras. In particular, we consider traces which vanish on nonzero…

Let $X=(V\!X,E\!X)$ be an infinite, locally finite, connected graph without loops or multiple edges. We consider the edges to be oriented, and $E\!X$ is equipped with an involution which inverts the orientation. Each oriented edge is…

For any finite directed graph $E$ and any field $K$ we show that the Cohn path algebra $C_K(E)$ has the Invariant Basis Number property.

We study the center of several types of path algebras. We start with the path algebra $KE$ and prove that if the number of vertices is infinite then the center is zero. Otherwise, it coincides with the field $K$ except when the graph $E$ is…

An infinite matroid is graphic if all of its finite minors are graphic and the intersection of any circuit with any cocircuit is finite. We show that a matroid is graphic if and only if it can be represented by a graph-like topological…