1 results
Group actions on Smale space
$\text{C}^{\ast }$-algebras
- Part of
-
- Journal:
- Ergodic Theory and Dynamical Systems / Volume 40 / Issue 9 / September 2020
- Published online by Cambridge University Press:
- 10 April 2019, pp. 2368-2398
- Print publication:
- September 2020
-
- Article
- Export citation
-
Group actions on a Smale space and the actions induced on the
$\text{C}^{\ast }$-algebras associated to such a dynamical system are studied. We show that an effective action of a discrete group on a mixing Smale space produces a strongly outer action on the homoclinic algebra. We then show that for irreducible Smale spaces, the property of finite Rokhlin dimension passes from the induced action on the homoclinic algebra to the induced actions on the stable and unstable 
$\text{C}^{\ast }$-algebras. In each of these cases, we discuss the preservation of properties (such as finite nuclear dimension, 
${\mathcal{Z}}$-stability, and classification by Elliott invariants) in the resulting crossed products.
