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 ´etale 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].
Topological Groupoid Quantales
RE, Riccardo
2010-01-01
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 ´etale 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].File in questo prodotto:
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