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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 579042, 7 pages
http://dx.doi.org/10.1155/2013/579042
Research Article

-Algebras from Groupoids on Self-Similar Groups

Department of Mathematics Education, Ewha Womans University, Seoul 120-750, Republic of Korea

Received 10 May 2013; Accepted 2 July 2013

Academic Editor: Salvador Hernandez

Copyright © 2013 Inhyeop Yi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 associated to a postcritically finite hyperbolic rational function is an AT-algebra of real-rank zero with a unique trace state.