• Corpus ID: 14754548

# The co-universal C*-algebra of a row-finite graph

@article{Sims2008TheCC,
title={The co-universal C*-algebra of a row-finite graph},
author={Aidan Sims},
journal={arXiv: Operator Algebras},
year={2008},
pages={507-524}
}
• A. Sims
• Published 13 September 2008
• Mathematics
• arXiv: Operator Algebras
Let E be a row-finite directed graph. We prove that there exists a C -algebra C min(E) with the following co-universal property: given any C -algebra B generated by a Toeplitz-Cuntz-Krieger E-family in which all the vertex projections are nonzero, there is a canonical ho- momorphism from B onto C min(E). We also identify when a homo- morphism from B to C min(E) obtained from the co-universal property is injective. When every loop in E has an entrance, C min(E) coincides with the graph C…
9 Citations
We consider when the universal C∗-algebras associated to separated graphs are exact. Specifically, for finite separated graphs we show that the universal C∗-algebra is exact if and only if the
We consider when the universal $C^*$-algebras associated to edge-colored directed graphs are exact. Specifically, for countable edge-colored directed graphs we show that the universal $C^*$-algebra
For a row-finite higher-rank graph �, we construct a higher-rank graph T� such that the Toeplitz algebra ofis isomorphic to the Cuntz-Krieger algebra of T�. We then prove that the higher-rank graph
• Mathematics
• 2017
We study the category of left unital graded modules over the Steinberg algebra of a graded ample Hausdorff groupoid. In the first part of the paper, we show that this category is isomorphic to the
Directed graphs and their higher-rank analogues provide an intuitive framework to study a class of C∗-algebras which we call graph algebras. The theory of graph algebras has been developed by a
• Mathematics
• 2016
In this article, we introduce Cohn path algebras of higher-rank graphs. We prove that for a higher-rank graph Λ, there exists a higher-rank graph T Λ such that the Cohn path algebra of Λ is
• Mathematics
Algebras and Representation Theory
• 2016
In this article, we introduce Cohn path algebras of higher-rank graphs. We prove that for a higher-rank graph Λ, there exists a higher-rank graph T Λ such that the Cohn path algebra of Λ is
• Mathematics
• 2017
We consider Toeplitz and Cuntz-Krieger $C^*$-algebras associated with finitely aligned left cancellative small categories. We pay special attention to the case where such a category arises as the

## References

SHOWING 1-10 OF 12 REFERENCES

• 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
• 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
• 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
We study the ideal structure of C*-algebras arising from C*-correspondences. We prove that gauge-invariant ideals of our C*-algebras are parameterized by certain pairs of ideals of original
• 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
• Mathematics
• 2002
For any countable directed graph E we describe the primitive ideal space of the corresponding generalized Cuntz-Krieger algebra C*(E).
The Policy Corntnittee was known as the Confcrcnce Organization of the Mathematical Scicnccs for a year or two before it was finally incorporated on 25 Frbruar~ 1960 in thr District of Columbia under the name Confercncc Board of the mathematical Sciences, Inc.
• Mathematics
Ergodic Theory and Dynamical Systems
• 1997
We construct a universal Cuntz–Krieger algebra ${\cal {AO}}_A$, which is isomorphic to the usual Cuntz–Krieger algebra ${\cal O}_A$ when $A$ satisfies condition $(I)$ of Cuntz and Krieger. The Cuntz
• 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

### MR1777234 (2001k:46084), Zbl 0976

• MR1777234 (2001k:46084), Zbl 0976