Equivalent groupoids have Morita equivalent Steinberg algebras

• Lisa Orloff Clark ^[1] ; Aidan Sims ^[2]
  1. [1] University of Otago

     University of Otago

     Nueva Zelanda

     
  2. [2] University of Wollongong

     University of Wollongong

     Australia

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 6 (June 2015), 2015, págs. 2062-2075
• Idioma: inglés
• Enlaces
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• Resumen

  • Let G and H be ample groupoids and let R be a commutative unital ring. We show that if G and H are equivalent in the sense of Muhly–Renault–Williams, then the associated Steinberg algebras are Morita equivalent. We deduce that collapsing a “collapsible subgraph” of a directed graph in the sense of Crisp and Gow does not change the Morita-equivalence class of the associated Leavitt path R -algebra, and therefore a number of graphical constructions which yield Morita equivalent C⁎-algebras also yield Morita equivalent Leavitt path algebras.