Abstract and Applied Analysis

C -Algebras from Groupoids on Self-Similar Groups

Inhyeop Yi

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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.

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Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 579042, 7 pages.

First available in Project Euclid: 26 February 2014

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Yi, Inhyeop. ${C}^{\ast }$ -Algebras from Groupoids on Self-Similar Groups. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 579042, 7 pages. doi:10.1155/2013/579042. https://projecteuclid.org/euclid.aaa/1393450165

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