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A class of simple C*-algebras arising from certain non-sofic subshifts

Published online by Cambridge University Press:  11 February 2010

KENGO MATSUMOTO
KENGO MATSUMOTO*
Affiliation:
Department of Mathematical Sciences, Yokohama City University, 22-2 Seto, Kanazawa-ku, Yokohama, 236-0027, Japan (email: kengo@yokohama-cu.ac.jp)
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Abstract

We present a class of subshifts ZN,N=1,2,…, whose associated C*-algebras 𝒪ZN are simple, purely infinite and not stably isomorphic to any Cuntz–Krieger algebra nor to the Cuntz algebra 𝒪∞. The class of the subshifts is the first example whose associated C*-algebras are not stably isomorphic to any Cuntz–Krieger algebra nor to the Cuntz algebra 𝒪∞. The subshifts ZN are coded systems whose languages are context free. We compute the topological entropy for the subshifts and show that a KMS-state (a state satisfying the Kubo–Martin–Schwinger condition) for gauge action on the associated C*-algebra 𝒪ZN exists if and only if the logarithm of the inverse temperature is the topological entropy for the subshift ZN, and the corresponding KMS-state is unique.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 2 , April 2011 , pp. 459 - 482
Copyright
Copyright © Cambridge University Press 2009

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