A class of simple C^*-algebras arising from certain nonsofic subshifts

2008/05/19 by Kengo Matsumoto, Matsumoto, Kengo
Mathematics · #37B10 #46L35 #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA) #math.DS #math.OA #msc:37B10 #msc:46L35

paper · pdf · doi:10.48550/arxiv.0805.2767

21 pages

arxiv created 2008/05/19 · arxiv updated 2009/12/01

Abstract

We present a class of subshifts Z_N, N = 1,2,... whose associated C^*-algebras \cal O_ZN are simple, purely infinite and not stably isomorphic to any Cuntz-Krieger algebra nor to Cuntz algebra. The class of the subshifts is the first examples whose associated C^*-algebras are not stably isomorphic to any Cuntz-Krieger algebra nor to Cuntz algebra. The subshifts Z_N are coded systems whose languages are context free. We compute the topological entropy for the subshifts and show that KMS-state for gauge action on the associated C^*-algebra \cal O_ZN exists if and only if the logarithm of the inverse temperature is the topological entropy for the subshift Z_N, and the corresponding KMS-state is unique.

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