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Reconstruction of graded groupoids from graded Steinberg algebras

Journal Article


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Abstract


  • We show how to reconstruct a graded ample Hausdorff groupoid with topologically principal neutrally graded component from the ring structure of its graded Steinberg algebra over any commutative integral domain with 1, together with the embedding of the canonical abelian subring of functions supported on the unit space. We deduce that diagonal-preserving ring isomorphism of Leavitt path algebras implies C∗-isomorphism of C∗-algebras for graphs E and F in which every cycle has an exit.

UOW Authors


  •   Ara, Pere (external author)
  •   Bosa Puigredon, Joan (external author)
  •   Hazrat, Roozbeh (external author)
  •   Sims, Aidan

Publication Date


  • 2017

Citation


  • Ara, P., Bosa, J., Hazrat, R. & Sims, A. (2017). Reconstruction of graded groupoids from graded Steinberg algebras. Forum Mathematicum, 29 (5), 1023-1037.

Scopus Eid


  • 2-s2.0-85028822878

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1860&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/858

Number Of Pages


  • 14

Start Page


  • 1023

End Page


  • 1037

Volume


  • 29

Issue


  • 5

Place Of Publication


  • Germany

Abstract


  • We show how to reconstruct a graded ample Hausdorff groupoid with topologically principal neutrally graded component from the ring structure of its graded Steinberg algebra over any commutative integral domain with 1, together with the embedding of the canonical abelian subring of functions supported on the unit space. We deduce that diagonal-preserving ring isomorphism of Leavitt path algebras implies C∗-isomorphism of C∗-algebras for graphs E and F in which every cycle has an exit.

UOW Authors


  •   Ara, Pere (external author)
  •   Bosa Puigredon, Joan (external author)
  •   Hazrat, Roozbeh (external author)
  •   Sims, Aidan

Publication Date


  • 2017

Citation


  • Ara, P., Bosa, J., Hazrat, R. & Sims, A. (2017). Reconstruction of graded groupoids from graded Steinberg algebras. Forum Mathematicum, 29 (5), 1023-1037.

Scopus Eid


  • 2-s2.0-85028822878

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1860&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/858

Number Of Pages


  • 14

Start Page


  • 1023

End Page


  • 1037

Volume


  • 29

Issue


  • 5

Place Of Publication


  • Germany