KMS states on the C*-algebra of a higher-rank graph and periodicity in the path space
@article{Huef2014KMSSO, title={KMS states on the C*-algebra of a higher-rank graph and periodicity in the path space}, author={Astrid an Huef and Marcelo Laca and Iain Raeburn and Aidan Sims}, journal={Journal of Functional Analysis}, year={2014}, volume={268}, pages={1840-1875} }
56 Citations
C*-algebras of self-similar actions of groupoids on higher-rank graphs and their equilibrium states.
- Mathematics
- 2019
We introduce the notion of a self-similar action of a groupoid G on a finite higher-rank graph. To these actions we associate a compactly aligned product system of Hilbert bimodules, and we show that…
A program for finding all KMS states on the Toeplitz algebra of a higher-rank graph
- MathematicsJournal of Operator Theory
- 2019
The Toeplitz algebra of a finite graph of rank k carries a natural action of the torus Tk, and composing with an embedding of R in Tk gives a dynamics on the Toeplitz algebra. In this paper we…
Perron-Frobenius theory and KMS states on higher-rank graph C*-Algebras
- Mathematics
- 2019
In this thesis, we study the Perron-Frobenius theory for irreducible matrices and irreducible family of commuting matrices in detail. We then apply it to study the KMS states of the C∗-algebras of…
Twisted k-Graph Algebras Associated to Bratteli Diagrams
- Mathematics
- 2014
Given a system of coverings of k-graphs, we show that the second cohomology of the resulting (k + 1)-graph is isomorphic to that of any one of the k-graphs in the system, and compute the semifinite…
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…
KMS states on the C*-algebras of Fell bundles over groupoids
- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 2019
Abstract We consider fibrewise singly generated Fell bundles over étale groupoids. Given a continuous real-valued 1-cocycle on the groupoid, there is a natural dynamics on the cross-sectional algebra…
Preferred traces on C⁎-algebras of self-similar groupoids arising as fixed points
- MathematicsJournal of Mathematical Analysis and Applications
- 2018
Irreducibility and monicity for representations of $k$-graph $C^*$-algebras
- Mathematics
- 2021
The representations of a k-graph C∗-algebra C∗(Λ) which arise from Λ-semibranching function systems are closely linked to the dynamics of the k-graph Λ. In this paper, we undertake a systematic…
Representations of higher-rank graph C⁎-algebras associated to Λ-semibranching function systems
- MathematicsJournal of Mathematical Analysis and Applications
- 2018
References
SHOWING 1-10 OF 41 REFERENCES
KMS states on the C*-algebras of reducible graphs
- Mathematics
- 2014
We consider the dynamics on the C*-algebras of finite graphs obtained by lifting the gauge action to an action of the real line. Enomoto, Fujii and Watatani proved that if the vertex matrix of the…
Factoriality and Type Classification of k-Graph von Neumann Algebras
- MathematicsProceedings of the Edinburgh Mathematical Society
- 2016
Abstract Let be a single vertex k-graph and let be the von Neumann algebra induced from the Gelfand–Naimark–Segal (GNS) representation of a distinguished state ω of its k-graph C*-algebra . In this…
A family of 2-graphs arising from two-dimensional subshifts
- MathematicsErgodic Theory and Dynamical Systems
- 2009
Abstract Higher-rank graphs (or k-graphs) were introduced by Kumjian and Pask to provide combinatorial models for the higher-rank Cuntz–Krieger C*-algebras of Robertson and Steger. Here we consider a…
KMS states on finite-graph C*-algebras
- Mathematics
- 2010
We study KMS states on finite-graph C*-algebras with sinks and sources. We compare finite-graph C*-algebras with C*-algebras associated with complex dynamical systems of rational functions. We show…
The primitive ideals of the Cuntz–Krieger algebra of a row-finite higher-rank graph with no sources ☆
- Mathematics
- 2014
Type III von Neumann algebras associated with 2‐graphs
- Mathematics
- 2011
Let 픽θ+ be a 2‐graph, where θ is a permutation encoding the factorization property in the 2‐graph, and ω be a distinguished faithful state associated with its graph C*‐algebra. In this paper, we…
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…
Actions of Z^k associated to higher rank graphs
- Mathematics
- 2014
An action of Z k is associated to a higher rank graph Λ satisfying a mild assumption. This generalizes the construction of a topological Markov shift arising from a non-negative integer matrix. We…