Topological Groupoid Quantales

A. Palmigiano*, R. Re

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


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 languageEnglish
Pages (from-to)125-137
Number of pages13
JournalStudia logica
Issue number1
Publication statusPublished - 1 Jul 2010
Externally publishedYes


  • étale groupoid
  • Penrose tilings
  • regular frame
  • representation theorem
  • topological groupoid
  • unital involutive quantale


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