C*-algebras from groupoids on self-similar groups

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We show that the Smale spaces from self-similar groups are topologically mixing and their stable algebra and stable Ruelle algebra are strongly Morita equivalent to groupoid algebras of Anantharaman-Delaroche and Deaconu. And we show that C* (R ∞) associated to a postcritically finite hyperbolic rational function is an AT-algebra of real-rank zero with a unique trace state.

Original languageEnglish
Article number579042
JournalAbstract and Applied Analysis
StatePublished - 2013


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