# KMS states on C⁎-algebras associated to higher-rank graphs☆

@article{Huef2012KMSSO, title={KMS states on C⁎-algebras associated to higher-rank graphs☆}, author={Astrid an Huef and Marcelo Laca and Iain Raeburn and Aidan Sims}, journal={Journal of Functional Analysis}, year={2012}, volume={266}, pages={265-283} }

## 53 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,…

### KMS states on the C*-algebra of a higher-rank graph and periodicity in the path space

- Mathematics
- 2014

### 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…

### 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…

### 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…

### Communications in Mathematical Physics KMS States on Nica-Toeplitz C ∗-algebras

- Mathematics
- 2020

Given a quasi-lattice ordered group (G, P) and a compactly aligned product system X of essential C∗-correspondences over the monoid P , we show that there is a bijection between the gauge-invariant…

### 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 of graph algebras with a generalised gauge dynamics

- Mathematics
- 2016

The goal of this thesis is to study the KMS states of graph algebras with a generalised gauge dynamics. We start by studying the KMS states of the Toeplitz algebra and graph algebra of a finite…

## 27 References

### Partial Dynamical Systems and the KMS Condition

- Mathematics
- 2000

Abstract: Given a countably infinite 0–1 matrix A without identically zero rows, let 𝒪A be the Cuntz–Krieger algebra recently introduced by the authors and 𝒯A be the Toeplitz extension of 𝒪A, once…

### 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…

### Phase transition on the Toeplitz algebra of the affine semigroup over the natural numbers

- Mathematics
- 2009

### Product systems of graphs and the Toeplitz algebras of higher-rank graphs | NOVA. The University of Newcastle's Digital Repository

- Mathematics
- 2003

There has recently been much interest in the C � -algebras of directed graphs. Here we consider product systems E of directed graphs over semigroups and associated C � -algebras C � (E) and T C � (E)…

### 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…

### 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…

### 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…

### Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory

- Mathematics
- 1995

In this paper, we construct a naturalC*-dynamical system whose partition function is the Riemann ζ function. Our construction is general and associates to an inclusion of rings (under a suitable…