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

@article{Carlsen2015OnHA,
  title={On Hong and Szymański’s Description of the Primitive-Ideal Space of a Graph Algebra},
  author={Toke Meier Carlsen and Aidan Sims},
  journal={arXiv: Operator Algebras},
  year={2015},
  pages={109-126}
}
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 context of row-finite graphs with no sources, obtaining an explicit description of the ideal lattice of a graph algebra. 

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

  • Hui Li
  • Mathematics
    Rocky 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 Ultragraph $C^*$-algebras

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

CONDITION (K) FOR BOOLEAN DYNAMICAL SYSTEMS

Abstract We generalize Condition (K) from directed graphs to Boolean dynamical systems and show that a locally finite Boolean dynamical system $({{\mathcal {B}}},{{\mathcal {L}}},\theta )$ with

References

SHOWING 1-10 OF 14 REFERENCES

The ideal structure of the $C\sp *$-algebras of infinite graphs

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

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

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

GRAPH C ∗ -ALGEBRAS WITH A T1 PRIMITIVE IDEAL SPACE

We give necessary and sufficient conditions which a graph should satisfy in order for its associated C ∗-algebra to have a T 1 primitive ideal space. We give a description of which one-point sets in

Graphs, Groupoids, and Cuntz–Krieger Algebras

We associate to each locally finite directed graphGtwo locally compact groupoidsGandG(★). The unit space ofGis the space of one–sided infinite paths inG, andG(★) is the reduction ofGto the space of

THE C -ALGEBRAS OF ROW-FINITE GRAPHS

NSKI Abstract. We prove versions of the fundamental theorems about Cuntz-Krieger algebras for the C -algebras of row-finite graphs: directed graphs in which each vertex emits at most finitely many

Morita Equivalence and Continuous-Trace $C^*$-Algebras

The algebra of compact operators Hilbert $C^*$-modules Morita equivalence Sheaves, cohomology, and bundles Continuous-trace $C^*$-algebras Applications Epilogue: The Brauer group and group actions

A stabilization theorem for Fell bundles over groupoids

We study the C *-algebras associated with upper semi-continuous Fell bundles over second-countable Hausdorff groupoids. Based on ideas going back to the Packer–Raeburn ‘stabilization trick’, we

CUNTZ-KRIEGER ALGEBRAS OF DIRECTED GRAPHS

We associate to each row-nite directed graph E a universal Cuntz-Krieger C-algebra C(E), and study how the distribution of loops in E aects the structure of C(E) .W e prove that C(E) is AF if and

The $C^*$-algebra generated by an isometry