scholarly journals KMS STATES ON FINITE-GRAPH C∗-ALGEBRAS

2013 ◽  
Vol 67 (1) ◽  
pp. 83-104 ◽  
Author(s):  
Tsuyoshi KAJIWARA ◽  
Yasuo WATATANI
Keyword(s):  
Finite Graph ◽  
Kms States ◽  
C Algebras

scholarly journals KMS states on C*-algebras associated to local homeomorphisms

2014 ◽  
Vol 25 (08) ◽  
pp. 1450066 ◽  
Author(s):  
Zahra Afsar ◽  
Astrid an Huef ◽  
Iain Raeburn
Keyword(s):  
Finite Graph ◽  
Critical Value ◽  
Toeplitz Algebra ◽  
Graph Algebras ◽  
Kms States ◽  
C Algebra ◽  
C Algebras ◽  
Backward Shift ◽  
The One ◽  
Natural Dynamics

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 lifting these gauge actions to actions of the real line. We study the KMS states of these dynamics for a family of bimodules associated to local homeomorphisms on compact spaces. For inverse temperatures larger than a certain critical value, we find a large simplex of KMS states on the Toeplitz algebra, and we show that all KMS states on the Cuntz–Pimsner algebra have inverse temperature at most this critical value. We illustrate our results by considering the backward shift on the one-sided path space of a finite graph, where we can use recent results about KMS states on graph algebras to see what happens below the critical value. Our results about KMS states on the Cuntz–Pimsner algebra of the shift show that recent constraints on the range of inverse temperatures obtained by Thomsen are sharp.

scholarly journals Spatial realisations of KMS states on the C⁎-algebras of higher-rank graphs

2015 ◽  
Vol 427 (2) ◽  
pp. 977-1003 ◽  
Author(s):  
Astrid an Huef ◽  
Sooran Kang ◽  
Iain Raeburn
Keyword(s):  
Kms States ◽  
C Algebras ◽  
Higher Rank

KMS states for gauge actions on $C^*$ -algebras associated with subshifts

1998 ◽  
Vol 228 (3) ◽  
pp. 489-509 ◽  
Author(s):  
Kengo Matsumoto ◽  
Yasuo Watatani ◽  
Masamichi Yoshida
Keyword(s):  
Kms States ◽  
C Algebras

scholarly journals KMS states on C*-algebras associated to expansive maps

2006 ◽  
Vol 134 (7) ◽  
pp. 2067-2078 ◽  
Author(s):  
Alex Kumjian ◽  
Jean Renault
Keyword(s):  
Kms States ◽  
C Algebras ◽  
Expansive Maps

scholarly journals KMS states of self-similar k-graph C*-algebras

2019 ◽  
Vol 276 (12) ◽  
pp. 3795-3831 ◽  
Author(s):  
Hui Li ◽  
Dilian Yang
Keyword(s):  
Kms States ◽  
C Algebras ◽  
Self Similar

scholarly journals Topological entropy for the canonical completely positive maps on graph C*-Algebras

2004 ◽  
Vol 70 (1) ◽  
pp. 101-116 ◽  
Author(s):  
Ja A. Jeong ◽  
Gi Hyun Park
Keyword(s):  
Topological Entropy ◽  
Finite Graph ◽  
Infinite Graph ◽  
Completely Positive Map ◽  
Completely Positive Maps ◽  
Completely Positive ◽  
Locally Finite ◽  
Finite Graphs ◽  
C Algebras ◽  
Positive Maps

Let C*(E) = C*(se, pv) be the graph C*-algebra of a directed graph E = (E0, E1) with the vertices E0 and the edges E1. We prove that if E is a finite graph (possibly with sinks) and φE: C*(E) → C*(E) is the canonical completely positive map defined by then Voiculescu's topological entropy ht(φE) of φE is log r(AE), where r(AE) is the spectral radius of the edge matrix AE of E. This extends the same result known for finite graphs with no sinks. We also consider the map φE when E is a locally finite irreducible infinite graph and prove that , where the supremum is taken over the set of all finite subgraphs of E.

scholarly journals Invariance of KMS states on graph C*-algebras under classical and quantum symmetry

2021 ◽  
pp. 1-17
Author(s):  
Soumalya Joardar ◽  
Arnab Mandal
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Inverse Temperature ◽  
Circulant Graphs ◽  
Connected Graphs ◽  
Kms States ◽  
C Algebras ◽  
Kms State ◽  
Quantum Symmetry ◽  
Strongly Connected

Abstract We study the invariance of KMS states on graph $C^{\ast }$ -algebras coming from strongly connected and circulant graphs under the classical and quantum symmetry of the graphs. We show that the unique KMS state for strongly connected graphs is invariant under the quantum automorphism group of the graph. For circulant graphs, it is shown that the action of classical and quantum automorphism groups preserves only one of the KMS states occurring at the critical inverse temperature. We also give an example of a graph $C^{\ast }$ -algebra having more than one KMS state such that all of them are invariant under the action of classical automorphism group of the graph, but there is a unique KMS state which is invariant under the action of quantum automorphism group of the graph.

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