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.
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References
SHOWING 1-10 OF 14 REFERENCES
The ideal structure of the $C\sp *$-algebras of infinite graphs
- Mathematics
- 2001
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 ideals of the Cuntz–Krieger algebra of a row-finite higher-rank graph with no sources ☆
- Mathematics
- 2014
The primitive ideal space of the $C^{*}$-algebras of infinite graphs
- Mathematics
- 2002
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
- Mathematics
- 2013
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
- Mathematics
- 1997
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
- Mathematics
- 2000
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
- Mathematics
- 1998
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
- MathematicsProceedings of the Royal Society of Edinburgh: Section A Mathematics
- 2017
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
- Mathematics
- 1998
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…