When is the Cuntz–Krieger algebra of a higher-rank graph approximately finite-dimensional?

@article{Evans2011WhenIT,
  title={When is the Cuntz–Krieger algebra of a higher-rank graph approximately finite-dimensional?},
  author={D. Gwion Evans and Aidan Sims},
  journal={Journal of Functional Analysis},
  year={2011},
  volume={263},
  pages={183-215}
}

Figures from this paper

Complex Kumjian-Pask algebras

Let Λ be a row-finite k-graph without sources. We investigate the relationship between the complex Kumjian-Pask algebra KPℂ(Λ) and graph algebra C*(Λ). We identify situations in which the

STABILITY OF C∗-ALGEBRAS ASSOCIATED TO k-GRAPHS

We give an emended proof of a result in the literature characterizing which graphs yield stable C∗-algebras. We strengthen this result by adding another necessary condition. We characterize stability

Some notes on complex Kumjian-Pask algebras of finitely aligned k-graphs

Suppose ۸ is a finitely aligned k-graph. In this paper we present some conditions for the k-graph ۸ in order the complex Kumjian-Pask algebra KPℂ(۸) is finite dimensional. This is an improvement for

Cycline subalgebras of $k$-graph C*-algebras

In this paper, we prove that the cycline subalgbra of a $k$-graph C*-algebra is maximal abelian, and show when it is a Cartan subalgebra (in the sense of Renault).

AF-embeddability of 2-graph algebras and stable finiteness of k-graph algebras

We characterise stable finiteness of the C*-algebra of a cofinal k-graph in terms of an algebraic condition involving the coordinate matrices of the graph. This result covers all simple k-graph

Twisted $C^*$-algebras associated to finitely aligned higher-rank graphs

We introduce twisted relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs and give a comprehensive treatment of their fundamental structural properties. We establish

Continuous-trace $k$-graph $C^*$-algebras

  • Danny Crytser
  • Mathematics
    Rocky Mountain Journal of Mathematics
  • 2018
A characterization is given for directed graphs that yield graph $C^*$-algebras with continuous trace. This is established for row-finite graphs with no sources first using a groupoid approach, and

Structure theory and stable rank for C*-algebras of finite higher-rank graphs

Abstract We study the structure and compute the stable rank of $C^{*}$-algebras of finite higher-rank graphs. We completely determine the stable rank of the $C^{*}$-algebra when the $k$-graph either

References

SHOWING 1-10 OF 60 REFERENCES

Relative Cuntz-Krieger algebras of finitely aligned higher-rank graphs

We define the relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs. We prove versions of the gauge-invariant unique- ness theorem and the Cuntz-Krieger uniqueness theorem

Higher-Rank Graph C *-Algebras: An Inverse Semigroup and Groupoid Approach

AbstractWe provide inverse semigroup and groupoid models for the Toeplitz and Cuntz-Krieger algebras of finitely aligned higher-rank graphs. Using these models, we prove a uniqueness theorem for the

HIGHER-RANK GRAPHS AND THEIR $C^*$-ALGEBRAS

Abstract We consider the higher-rank graphs introduced by Kumjian and Pask as models for higher-rank Cuntz–Krieger algebras. We describe a variant of the Cuntz–Krieger relations which applies to

SIMPLICITY OF FINITELY-ALIGNED k-GRAPH C -ALGEBRAS

It is shown that no local periodicity is equivalent to the aperiodicity condition for arbitrary nitely-aligned k-graphs. This allows us to conclude that C () is simple if and only if is conal and has

Every AF-algebra is Morita equivalent to a graph algebra

  • J. Tyler
  • Mathematics
    Bulletin of the Australian Mathematical Society
  • 2004
We show how to modify any Bratteli diagram E for an AF-algebra A to obtain a Bratteli diagram KE for A whose graph algebra C*(KE) contains both A and C*(E) as full corners.

Non-commutative spheres

LetAθ be the irrational rotation algebra, i.e. theC*-algebra generated by two unitariesU, V satisfyingVU=e2πiθUV, with θ irrational, and consider the fixed point subalgebraBθ under the flip

Simplicity of C*‐algebras associated to higher‐rank graphs

We prove that if Λ is a row‐finite k‐graph with no sources, then the associated C*‐algebra is simple if and only if Λ is cofinal and satisfies Kumjian and Pask's aperiodicity condition, known as

Higher Rank Graph C-Algebras

Building on recent work of Robertson and Steger, we associate a C{algebra to a combinatorial object which may be thought of as a higher rank graph. This C{algebra is shown to be isomorphic to that of

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).

Cuntz-Krieger Algebras of Infinite Graphs and Matrices

We show that the Cuntz-Krieger algebras of infinite graphs and infinite {0,1}-matrices can be approximated by those of finite graphs. We then use these approximations to deduce the main uniqueness
...