Related papers: Primitive ideal space of Higher-rank graph $C^*$-a…

We determine the primitive ideal space and hence the ideal lattice of a large class of separable groupoid C*-algebras that includes all 2-graph C*-algebras. A key ingredient is the notion of harmonious families of bisections in etale…

Given a directed graph $E$ and a labeling $\mathcal{L}$, one forms the labelled graph $C^*$-algebra by taking a weakly left--resolving labelled space $(E, \mathcal{L}, \mathcal{B})$ and considering a universal generating family of partial…

Let $(G, \Lambda)$ be a self-similar $k$-graph with a possibly infinite vertex set $\Lambda^0$. We associate a universal C*-algebra $\mathcal{O}_{G,\Lambda}$ to $(G,\Lambda)$. The main purpose of this paper is to investigate the ideal…

We produce a complete descrption of the lattice of gauge-invariant ideals in $C^*(\Lambda)$ for a finitely aligned $k$-graph $\Lambda$. We provide a condition on $\Lambda$ under which every ideal is gauge-invariant. We give conditions on…

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 describe the primitive ideal space of the $C^{\ast}$-algebra of a row-finite $k$-graph with no sources when every ideal is gauge invariant. We characterize which spectral spaces can occur, and compute the primitive ideal space of two…

In previous work, the authors showed that the C*-algebra C*(\Lambda) of a row-finite higher-rank graph \Lambda with no sources is simple if and only if \Lambda is both cofinal and aperiodic. In this paper, we generalise this result to…

In 2004, Hong and Szymanski gave a complete description of the primitive-ideal space of the C*-algebra of a directed graph. This article details a slightly different approach, in the simpler context of row-finite graphs with no sources,…

For any countable directed graph E we describe the primitive ideal space of the corresponding generalized Cuntz-Krieger algebra C*(E).

We describe the Jacobson topology of the primitive ideal space of self-similar k-graph C*-algebras under certain conditions.

We give a complete description of the primitive ideal space of the C*-algebra associated to the ring of integers R in a number field K as considered in a recent paper by Cuntz, Deninger and Laca.

In this paper, we discuss a method of constructing separable representations of the $C^*$-algebras associated to strongly connected row-finite $k$-graphs $\Lambda$. We begin by giving an alternative characterization of the…

We obtained a "decomposition scheme" of C*-algebras. We show that the classes of discrete C*-algebras (as defined by Peligard and Zsido), type II C*-algebras and type III C*-algebras (both defined by Cuntz and Pedersen) form a good…

We give necessary and sufficient conditions which a graph should satisfy in order for its associated $C^\ast$-algebra to have a $T_1$ primitive ideal space. We give a description of which one-point sets in such a primitive ideal space are…

In this paper we generalize the notion of a $k$-graph into (countable) infinite rank. We then define our $C^*$-algebra in a similar way as in $k$-graph $C^*$-algebras. With this construction we are able to find analogues to the Gauge…

We classify the gauge-invariant ideals in the C*-algebras of infinite directed graphs, and describe the quotients as graph algebras. We then use these results to identify the gauge-invariant primitive ideals in terms of the structural…

Counterexamples to classification of purely infinite, nuclear, separable C*-algebras (in the ideal-related bootstrap class) and with primitive ideal space X using ideal-related K-theory occur for infinitely many finite primitive ideal…

Radial representations of finitely generated free groups are studied. The associated C*-algebra is located between the reduced and full group C*-algebras and its primitive ideal space is described concretely as a topological space.

The representations of a $k$-graph $C^*$-algebra $C^*(\Lambda)$ which arise from $\Lambda$-semibranching function systems are closely linked to the dynamics of the $k$-graph $\Lambda$. In this paper, we undertake a systematic analysis of…

In this monograph we undertake a comprehensive study of separable representations (as well as their unitary equivalence classes) of $C^*$-algebras associated to strongly connected finite $k$-graphs $\Lambda$. We begin with the…