Abstract
In this paper, we study inverse semigroups defined on the Bratteli–Vershik systems and SFT covers of 1-solenoids. We show that groupoids of germs of these inverse semigroups are equivalent to the unstable equivalence groupoids of 1-solenoids. Then we prove that Exel’s tight C∗-algebras of inverse semigroups are strongly Morita equivalent to the unstable C∗-algebras of 1-solenoids.
| Original language | English |
|---|---|
| Pages (from-to) | 81-104 |
| Number of pages | 24 |
| Journal | Semigroup Forum |
| Volume | 96 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Feb 2018 |
Bibliographical note
Publisher Copyright:© 2017, Springer Science+Business Media New York.
Keywords
- 1-Solenoid
- Bratteli–Vershik system
- Groupoid of germs
- Inverse semigroup
- Smale space
- Tight groupoid