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} }
33 Citations
Complex Kumjian-Pask algebras
- MathematicsActa Mathematica Sinica, English Series
- 2013
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
- Mathematics
- 2014
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
- Mathematics
- 2017
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
- Mathematics
- 2015
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
- Mathematics
- 2015
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
- MathematicsDocumenta Mathematica
- 2014
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
- MathematicsRocky 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
- MathematicsProceedings of the Edinburgh Mathematical Society
- 2021
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
- Mathematics
- 2003
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
- Mathematics
- 2004
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
- MathematicsProceedings of the Edinburgh Mathematical Society
- 2003
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
- Mathematics
- 2008
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
- MathematicsBulletin 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
- Mathematics
- 1992
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
- Mathematics
- 2007
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
- Mathematics
- 2000
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
- Mathematics
- 2002
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
- Mathematics
- 2003
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…