# KMS states on the C∗-algebras of finite graphs

@article{Huef2012KMSSO, title={KMS states on the C∗-algebras of finite graphs}, author={Astrid an Huef and Marcelo Laca and Iain Raeburn and Aidan Sims}, journal={Journal of Mathematical Analysis and Applications}, year={2012}, volume={405}, pages={388-399} }

## 50 Citations

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

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### Equilibrium states on graph algebras

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We consider operator-algebraic dynamical systems given by actions of the real line on unital C∗-algebras, and especially the equilibrium states (or KMS states) of such systems. We are particularly…

### Reconstructing directed graphs from generalized gauge actions on their Toeplitz algebras

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Abstract We show how to reconstruct a finite directed graph E from its Toeplitz algebra, its gauge action, and the canonical finite-dimensional abelian subalgebra generated by the vertex projections.…

### Limits of KMS states on Toeplitz algebras of finite graphs

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- 2021

The structure of KMS states of Toeplitz algebras associated to finite graphs equipped with the gauge action is determined by an Huef–Laca–Raeburn–Sims. Their results imply that extremal KMS states of…

### KMS states on C ⁎ -algebras associated to a family of ⁎-commuting local homeomorphisms

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### 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 C*-algebras associated to local homeomorphisms

- Mathematics
- 2014

For every Hilbert bimodule over a C*-algebra, there are natural gauge actions of the circle on the associated Toeplitz algebra and Cuntz–Pimsner algebra, and hence natural dynamics obtained by…

### C*-dynamical invariants and Toeplitz algebras of graphs

- Mathematics
- 2021

In recent joint work of the authors with Laca, we precisely formulated the notion of partition function in the context of C*-dynamical systems. Here, we compute the partition functions of…

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We describe KMS-states on the C -algebras of etale groupoids in terms of measurable elds of traces on the C -algebras of the isotropy groups. We use this description to analyze tracial states on the…

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- Mathematics
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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…

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Suppose a C*-algebra A acts by adjointable operators on a Hilbert A-module X. Pimsner constructed a C*-algebra O_X which includes, for particular choices of X, crossed products of A by Z, the Cuntz…

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Using Walters' version of the Ruelle-Perron-Frobenius Theorem we show the existence and uniqueness of KMS states for a certain one-parameter group of automorphisms on a C*-algebra associated to a…

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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…

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We develop a theory of graph C -algebras using path groupoids and inverse semigroups. Row finiteness is not assumed so that the theory applies to graphs for which there are vertices emitting a…

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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…

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- Mathematics
- 2004

In this paper, we study KMS states for the gauge actions on
C${}^*$-algebras associated with self-similar sets whose branch points are finite. If the self-similar set does not contain any branch…