Morita equivalence of groupoid $C^*$-algebras arising from dynamical systems
Volume 149 / 2002
Studia Mathematica 149 (2002), 121-132
MSC: 46L05, 46L80, 46L89.
DOI: 10.4064/sm149-2-3
Abstract
We show that the stable $C^*$-algebra and the related Ruelle algebra defined by I. Putnam from the irreducible Smale space associated with a topologically mixing expanding map of a compact metric space are strongly Morita equivalent to the groupoid $C^*$-algebras defined directly from the expanding map by C. Anantharaman-Delaroche and V. Deaconu. As an application, we calculate the $K_*$-group of the Ruelle algebra for a solenoid.
