A class of simple $C^{\ast }$-algebras arising from certain nonsofic subshifts

Abstract

We present a class of subshifts $Z_N,N=1,2,...$ whose associated $C^{\ast }$-algebras ${\mathcal{O}}_{Z_N}$ 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 $C^{\ast }$-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 $C^{\ast }$-algebra ${\mathcal{O}}_{Z_N}$ 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.

21 pages