The primitive ideals of the Cuntz–Krieger algebra of a row-finite higher-rank graph with no sources ☆
@article{Carlsen2013ThePI, title={The primitive ideals of the Cuntz–Krieger algebra of a row-finite higher-rank graph with no sources ☆}, author={Toke Meier Carlsen and Sooran Kang and J. Arnold Shotwell and Aidan Sims}, journal={Journal of Functional Analysis}, year={2013}, volume={266}, pages={2570-2589} }
45 Citations
Simplicity of twisted C*-algebras of higher-rank graphs and crossed products by quasifree actions
- Mathematics
- 2014
We characterise simplicity of twisted C*-algebras of row-finite k-graphs with no sources. We show that each 2-cocycle on a cofinal k-graph determines a canonical second-cohomology class for the…
KMS states on the C*-algebra of a higher-rank graph and periodicity in the path space
- Mathematics
- 2014
The structure of higher rank graph C*-algebras revisited
- Mathematics
- 2014
In this paper, we study a higher rank graph, which has a period group deduced from a natural equivalence relation on its infinite path space. We prove that the C*-algebra generated by the standard…
GRAPHS AND CROSSED PRODUCTS BY QUASIFREE ACTIONS
- Mathematics
- 2014
We characterise simplicity of twisted C � -algebras of row-finite k-graphs with no sources. We show that each 2-cocycle on a cofinal k-graph determines a canonical second-cohomology class for the…
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…
Von Neumann algebras of strongly connected higher-rank graphs
- Mathematics
- 2014
We investigate the factor types of the extremal KMS states for the preferred dynamics on the Toeplitz algebra and the Cuntz–Krieger algebra of a strongly connected finite $$k$$k-graph. For inverse…
Monic representations of finite higher-rank graphs
- MathematicsErgodic Theory and Dynamical Systems
- 2020
In this paper, we define the notion of monic representation for the $C^{\ast }$-algebras of finite higher-rank graphs with no sources, and we undertake a comprehensive study of them. Monic…
Computing the fundamental group of a higher-rank graph
- MathematicsProceedings of the Edinburgh Mathematical Society
- 2021
Abstract We compute a presentation of the fundamental group of a higher-rank graph using a coloured graph description of higher-rank graphs developed by the third author. We compute the fundamental…
On Hong and Szymański’s Description of the Primitive-Ideal Space of a Graph Algebra
- Mathematics
- 2016
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…
References
SHOWING 1-10 OF 31 REFERENCES
Aperiodicity and the primitive ideal space of a row-finite $k$-graph $C^*$-algebra
- Mathematics
- 2011
We describe the primitive ideal space of the C � -algebra of a row-finite k-graph with no sources when every ideal is gauge invariant. We characterize which spectral spaces can occur, and compute 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…
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…
Affine buildings, tiling systems and higher rank Cuntz-Krieger algebras
- Mathematics
- 1999
To an $r$-dimensional subshift of finite type satisfying certain special properties we associate a $C^*$-algebra $\cA$. This algebra is a higher rank version of a Cuntz-Krieger algebra. In…
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…
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 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…
On higher rank graph C ∗ -algebras
- Mathematics
- 2000
Given a row-finite k-graph Λ with no sources we investigate the K-theory of the higher rank graph C *-algebra, C * (Λ). When k = 2 we are able to give explicit formulae to calculate the K-groups of C…
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…
Stable rank and real rank of graph C*-algebras
- Mathematics
- 2001
For a row finite directed graph E, Kumjian, Pask, and Raeburn proved that there exists a universal C*-algebra C* (E) generated by a Cuntz-Krieger E-family. In this paper we consider two density…