Reconstruction of graded groupoids from graded Steinberg algebras

Pere Ara, Joan Bosa, Roozbeh Hazrat, Aidan Sims

Research output: Contribution to journalArticleResearchpeer-review

13 Citations (Scopus)

Abstract

© 2017 Walter de Gruyter GmbH, Berlin/Boston 2017. 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.
Original languageEnglish
Pages (from-to)1023-1037
JournalForum Mathematicum
Volume29
Issue number5
DOIs
Publication statusPublished - 1 Sep 2017

Keywords

  • -algebra
  • C
  • Leavitt path algebra
  • Steinberg algebra
  • ample groupoid

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