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Communications in Mathematical Physics

, Volume 232, Issue 2, pp 223–277 | Cite as

Partial Dynamical Systems and the KMS Condition

  • Ruy Exel
  • Marcelo Laca

Abstract:

 Given a countably infinite 0–1 matrix A without identically zero rows, let 𝒪 A be the Cuntz–Krieger algebra recently introduced by the authors and 𝒯 A be the Toeplitz extension of 𝒪 A , once the latter is seen as a Cuntz–Pimsner algebra, as recently shown by Szymański. We study the KMS equilibrium states of C * -dynamical systems based on 𝒪 A and 𝒯 A , with dynamics satisfying \(\) for the canonical generating partial isometries s x and arbitrary real numbers N x > 1. The KMSβ states on both 𝒪 A and 𝒯 A are completely characterized for certain values of the inverse temperature β, according to the position of β relative to three critical values, defined to be the abscissa of convergence of certain Dirichlet series associated to A and the N(x). Our results for 𝒪 A are derived from those for 𝒯 A by virtue of the former being a covariant quotient of the latter. When the matrix A is finite, these results give theorems of Olesen and Pedersen for 𝒪 n and of Enomoto, Fujii and Watatani for 𝒪 A as particular cases.

Keywords

Dynamical System Real Number Equilibrium State Inverse Temperature Dirichlet Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Ruy Exel
    • 1
  • Marcelo Laca
    • 2
  1. 1.Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-900 Florianópolis SC, BrazilBR
  2. 2.Department of Mathematics, University of Newcastle, NSW 2308, Australia.AU

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