# 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

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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…