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

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dc.creatorMatsumoto, Kengo
dc.date2008-05-19
dc.date.accessioned2026-07-07T09:39:40Z
dc.date.available2026-07-07T09:39:40Z
dc.descriptionWe 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.
dc.description21 pages
dc.identifierhttps://arxiv.org/abs/0805.2767
dc.identifierhttp://arxiv.org/abs/0805.2767
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161257
dc.subjectOperator Algebras
dc.subjectDynamical Systems
dc.subject46L35; 37B10
dc.titleA class of simple $C^*$-algebras arising from certain nonsofic subshifts
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