C∗‐Algebras from Groupoids on Self‐Similar Groups

Inhyeop Yi

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: 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.

Date: 2013
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https://doi.org/10.1155/2013/579042

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:579042

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