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Equivalent groupoids have Morita equivalent Steinberg algebras

Journal Article


Abstract


  • 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.

UOW Authors


  •   Clark, Lisa Orloff (external author)
  •   Sims, Aidan

Publication Date


  • 2015

Citation


  • Clark, L. & Sims, A. D. (2015). Equivalent groupoids have Morita equivalent Steinberg algebras. Journal of Pure and Applied Algebra, 219 (6), 2062-2075.

Scopus Eid


  • 2-s2.0-84921022883

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/3473

Has Global Citation Frequency


Number Of Pages


  • 13

Start Page


  • 2062

End Page


  • 2075

Volume


  • 219

Issue


  • 6

Place Of Publication


  • Netherlands

Abstract


  • 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.

UOW Authors


  •   Clark, Lisa Orloff (external author)
  •   Sims, Aidan

Publication Date


  • 2015

Citation


  • Clark, L. & Sims, A. D. (2015). Equivalent groupoids have Morita equivalent Steinberg algebras. Journal of Pure and Applied Algebra, 219 (6), 2062-2075.

Scopus Eid


  • 2-s2.0-84921022883

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/3473

Has Global Citation Frequency


Number Of Pages


  • 13

Start Page


  • 2062

End Page


  • 2075

Volume


  • 219

Issue


  • 6

Place Of Publication


  • Netherlands