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

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

2008-05-19

arxiv.org/abs/0805.2767v1

Mathematics

Operator Algebras

21 pages

Scientific paper

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

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