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KMS state — 1 results found.

      
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KMS States for the Generalized Gauge Action on Graph Algebras
C. R. Math. Rep. Acad. Sci. Canada Vol. 36 (4) 2014, pp. 114–128
Gilles G. de Castro; Fernando de L. Mortari (Received: 2014/05/17, Revised: 2014/07/10)

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Given a positive function on the set of edges of an arbitrary directed graph \(E=(E^0,E^1)\), we define a one-parameter group of automorphisms on the C*-algebra of the graph \(C^*(E)\), and study the problem of finding KMS states for this action. We prove that there are bijective correspondences between KMS states on \(C^*(E)\), a certain class of states on its core, and a certain class of tracial states on \(C_0(E^0)\). We also find the ground states for this action and give some examples.

Étant donné une fonction positive sur l’ensemble des arcs d’un graphe orienté arbitraire \(E=(E^0,E^1)\), nous définissons un groupe à un paramètre d’automorphismes de la \(C^*\)-algèbre du graphe \(C^*(E)\), et nous étudions le problème de trouver les états KMS pour cette action. Nous prouvons qu’il existe des bijections entre les états KMS sur \(C^*(E)\), une certaine classe d’états sur le core, et une certaine classe détats traciaux sur \(C_0(E^0)\). Nous trouvons également les états fondamentaux pour cette action et nous donnons quelques exemples.

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