# The primitive ideal space of the $C^{*}$-algebras of infinite graphs

@article{Hong2002ThePI, title={The primitive ideal space of the \$C^\{*\}\$-algebras of infinite graphs}, author={Jeong Hee Hong and Wojciech Szymański}, journal={Journal of The Mathematical Society of Japan}, year={2002}, volume={56}, pages={45-64} }

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

## 64 Citations

### Jacobson topology of the primitive ideal space of self-similar k-graph C*-algebras

- MathematicsRocky Mountain Journal of Mathematics
- 2020

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

### Primitive ideal space of higher-rank graph C⁎-algebras and decomposability

- Mathematics, Computer ScienceJournal of Mathematical Analysis and Applications
- 2019

### Decomposability of graph C-algebras

- Mathematics
- 2004

We give conditions on an arbitrary directed graph E for the associated Cuntz-Krieger algebra C*(E) to be decomposable as a direct sum. We describe the direct summands as certain graph algebras.

### The prime spectrum and primitive ideal space of a graph C*-algebra

- Mathematics
- 2014

We describe primitive and prime ideals in the C*-algebra C*(E) of a graph E satisfying Condition (K), together with the topologies on each of these spaces. In particular, we find that primitive…

### On crossed products of the Cuntz algebra ${\mathcal O}_\infty$ by quasi-free actions of abelian groups

- Mathematics
- 2001

We investigate the structures of crossed products of the Cuntz algebra ${\mathcal O}_\infty$ by quasi-free actions of abelian groups. We completely determine their ideal structures and compute the…

### Gauge-Invariant Ideals in the C*-Algebras of Finitely Aligned Higher-Rank Graphs

- MathematicsCanadian Journal of Mathematics
- 2006

Abstract We produce a complete description of the lattice of gauge-invariant ideals in ${{C}^{*}}(\Lambda )$ for a finitely aligned $k$ -graph $\Lambda $ . We provide a condition on $\Lambda $ under…

### Stable rank of graph algebras. Type I graph algebras and their limits

- Mathematics
- 2002

For an arbitrary countable directed graph E we show that the only possible values of the stable rank of the associated Cuntz-Krieger algebra C* (E) are 1, 2 or ∞. Explicit criteria for each of these…

### On Hong and Szymański’s Description of the Primitive-Ideal Space of a Graph Algebra

- Mathematics
- 2016

In 2004, Hong and Szymanski produced 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…

### A class of C*-algebras generalizing both graph algebras and homeomorphism C*-algebras I, fundamental results

- Mathematics
- 2002

We introduce a new class of C*-algebras, which is a generalization of both graph algebras and homeomorphism C*-algebras. This class is very large and also very tractable. We prove the so-called…

### The Primitive Ideals of some Étale Groupoid C∗-Algebras

- Mathematics
- 2015

We consider the Deaconu–Renault groupoid of an action of a finitely generated free abelian monoid by local homeomorphisms of a locally compact Hausdorff space. We catalogue the primitive ideals of…

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We investigate the structures of crossed products of the Cuntz algebra ${\mathcal O}_\infty$ by quasi-free actions of abelian groups. We completely determine their ideal structures and compute the…

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