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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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
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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…
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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…