# 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

### KMS States on the Operator Algebras of Reducible Higher-Rank Graphs

- Mathematics
- 2016

We study the equilibrium or KMS states of the Toeplitz $$C^*$$C∗-algebra of a finite higher-rank graph which is reducible. The Toeplitz algebra carries a gauge action of a higher-dimensional torus,…

### 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…

### 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…

### 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…

### 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…

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- 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…

### 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…

### 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…

### The primitive ideals of the Cuntz–Krieger algebra of a row-finite higher-rank graph with no sources ☆

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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…

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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…

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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…

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We prove that there is a Poincare type duality in E-theory between higher rank graph algebras associated with a higher rank graph and its opposite correspondent. We obtain an r-duality, that is the…