# Ultragraph C -algebras via topological quivers

@article{Katsura2006UltragraphC, title={Ultragraph C -algebras via topological quivers}, author={Takeshi Katsura and Paul S. Muhly and Aidan Sims and Mark Tomforde}, journal={Studia Mathematica}, year={2006}, volume={187}, pages={137-155} }

Given an ultragraph in the sense of Tomforde, we construct a topological quiver in the sense of Muhly and Tomforde in such a way that the universal C -algebras associated to the two objects coincide. We apply results of Muhly and Tomforde for topological quiver algebras and of Katsura for topological graph C -algebras to study the K-theory and gauge-invariant ideal structure of ultragraph C -algebras.

## 21 Citations

### Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence

- Mathematics
- 2008

Abstract We prove that the classes of graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence. This result answers the long-standing open question of whether…

### KMS states and continuous orbit equivalence for ultragraph shift spaces with sinks

- MathematicsPublicacions Matemàtiques
- 2022

We extend ultragraph shift spaces and the realization of ultragraph C*-algebras as partial crossed products to include ultragraphs with sinks (under a mild condition, called (RFUM2), which allow us…

### THE C*-ALGEBRAS OF LATTICE ATOMIC GRAPHS

- MathematicsBulletin of the Australian Mathematical Society
- 2009

Abstract In this article, we define lattice graphs (which generalise ultragraphs) as well as their Cuntz–Krieger families and C*-algebras. We will give a thorough study in the special case of lattice…

### Realizations of AF-algebras as graph algebras, Exel-Laca algebras, and ultragraph algebras

- Mathematics
- 2008

### Primitive Ideal Space of Ultragraph $C^*$-algebras

- Mathematics
- 2019

In this paper, we describe the primitive ideal space of the $C^*$-algebra $C^*(mathcal G)$ associated to the ultragraph $mathcal{G}$. We investigate the structure of the closed ideals of the…

### Topological full groups of ultragraph groupoids as an isomorphism invariant

- Mathematics
- 2019

We prove two isomorphism-invariance theorems for groupoids associated with ultragraphs. These theorems characterize ultragraphs for which the topological full group of an associated groupoid is an…

### Ultragraph algebras via labelled graph groupoids, with applications to generalized uniqueness theorems

- Mathematics
- 2020

### The ideal structure of partial skew groupoid rings with applications to topological dynamics and ultragraph algebras

- Mathematics
- 2022

Given a partial action α of a groupoid G on a ring R , we study the associated partial skew groupoid ring R ⋊ α G , which carries a natural G -grading. We show that there is a one-to-one…

### 2 2 D ec 2 01 9 Topological full groups of ultragraphs groupoids as an isomorphism invariant

- Mathematics
- 2019

We prove two isomorphism-invariance theorems for groupoids associated with ultragraphs. These theorems characterize ultragraphs for which the topological full group of an associated groupoid is an…

### Groupoid and inverse semigroup presentations of ultragraph C*-algebras

- Mathematics
- 2007

AbstractInspired by the work of Paterson on C*-algebras of directed graphs, we show how to associate a groupoid
$\mathfrak{G}_{\mathcal{G}}$
to an ultragraph
$\mathcal{G}$
in such a way that the…

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