We associate a canonical unital involutive quantale to a topological groupoid. When the groupoid is also etale, 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, R.
2010-01-01

Abstract

We associate a canonical unital involutive quantale to a topological groupoid. When the groupoid is also etale, 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].
2010
étale groupoid; Penrose tilings; regular frame; representation theorem; topological groupoid; unital involutive quantale; Logic
Palmigiano, A.; Re, R.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2067710
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