Abstract
We associate a canonical unital involutive quantale to a topological groupoid. When the groupoid is also étale, this association is compatible with but independent from the theory of localic étale groupoids and their quantales [9] of P. Resende. As a motivating example, we describe the connection between the quantale and the C*-algebra that both classify Penrose tilings, which was left as an open problem in [5].
| Original language | English |
|---|---|
| Pages (from-to) | 125-137 |
| Number of pages | 13 |
| Journal | Studia logica |
| Volume | 95 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Jul 2010 |
| Externally published | Yes |
Keywords
- étale groupoid
- Penrose tilings
- regular frame
- representation theorem
- topological groupoid
- unital involutive quantale