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Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C*-algebras and Leavitt path algebras

Journal Article


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Abstract


  • We prove that ample groupoids with σ-compact unit spaces are equivalent if and only if they are stably isomorphic in an appropriate sense, and relate this to Matui's notion of Kakutani equivalence. We use this result to show that diagonal-preserving stable isomorphisms of graph C*-algebras or Leavitt path algebras give rise to isomorphisms of the groupoids of the associated stabilised graphs. We deduce that the Leavitt path algebras LZ(E2) and LZ(E2-) are not stably *-isomorphic.

Authors


  •   Carlsen, Toke Meier. (external author)
  •   Ruiz, Efren (external author)
  •   Sims, Aidan D.

Publication Date


  • 2017

Citation


  • Carlsen, T. Meier., Ruiz, E. & Sims, A. (2017). Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C*-algebras and Leavitt path algebras. Proceedings of the American Mathematical Society, 145 (4), 1581-1592.

Scopus Eid


  • 2-s2.0-85010756891

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=7447&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6417

Has Global Citation Frequency


Number Of Pages


  • 11

Start Page


  • 1581

End Page


  • 1592

Volume


  • 145

Issue


  • 4

Place Of Publication


  • United States

Abstract


  • We prove that ample groupoids with σ-compact unit spaces are equivalent if and only if they are stably isomorphic in an appropriate sense, and relate this to Matui's notion of Kakutani equivalence. We use this result to show that diagonal-preserving stable isomorphisms of graph C*-algebras or Leavitt path algebras give rise to isomorphisms of the groupoids of the associated stabilised graphs. We deduce that the Leavitt path algebras LZ(E2) and LZ(E2-) are not stably *-isomorphic.

Authors


  •   Carlsen, Toke Meier. (external author)
  •   Ruiz, Efren (external author)
  •   Sims, Aidan D.

Publication Date


  • 2017

Citation


  • Carlsen, T. Meier., Ruiz, E. & Sims, A. (2017). Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C*-algebras and Leavitt path algebras. Proceedings of the American Mathematical Society, 145 (4), 1581-1592.

Scopus Eid


  • 2-s2.0-85010756891

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=7447&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6417

Has Global Citation Frequency


Number Of Pages


  • 11

Start Page


  • 1581

End Page


  • 1592

Volume


  • 145

Issue


  • 4

Place Of Publication


  • United States