# 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}
}
• Published 11 November 2002
• Mathematics
• Journal of The Mathematical Society of Japan
For any countable directed graph E we describe the primitive ideal space of the corresponding generalized Cuntz-Krieger algebra C*(E).
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## References

SHOWING 1-10 OF 29 REFERENCES

• 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
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
For an arbitrary directed graph E and a *-homomorphism ϕ of the graph C*-algebra C*(E) we give a necessary and sufficient condition of injectivity of ϕ.
• Mathematics
• 2000
To an arbitrary directed graph we associate a row-finite directed graph whose C*-algebra contains the C*-algebra of the original graph as a full corner. This allows us to generalize results for
• Mathematics
• 2003
For arbitrary infinite directed graphs E, the characterisation of the (not necessarily simple) Cuntz–Krieger algebras C*(E) which are purely infinite in the sense of Kirchberg–Rørdam is given. It is
Abstract We completely determine the ideal structures of the crossed products of Cuntz algebras by quasi-free actions of abelian groups and give another proof of A. Kishimoto's result on the
We develop a theory of graph C -algebras using path groupoids and inverse semigroups. Row finiteness is not assumed so that the theory applies to graphs for which there are vertices emitting a
In this paper we analyze the structure of C*-algebras associated to ultragraphs, which are generalizations of directed graphs. We characterize the simple ultragraph algebras as well as deduce
• Mathematics
• 1998
Suppose a C*-algebra A acts by adjointable operators on a Hilbert A-module X. Pimsner constructed a C*-algebra O_X which includes, for particular choices of X, crossed products of A by Z, the Cuntz
• Mathematics
• 1999
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