Groupoid models of c-algebras and the gelfand functor

Kyle Austin, Atish Mitra

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We construct a large class of morphisms, which we call partial morphisms, of groupoids that induce ∗-morphisms of maximal and minimal groupoid C-algebras. We show that the assignment of a groupoid to its maximal (minimal) groupoid C-algebra and the assignment of a partial morphism to its induced morphism are functors (both of which extend the Gelfand functor). We show how to geomet-rically visualize lots of ∗-morphisms between groupoid C-algebras. As an application, we construct, without any use of the classification the-ory, groupoid models of the entire inductive systems used in the original constructions of the Jiang-Su algebra Z and the Razak-Jacelon algebra W. Consequently, the inverse limit of the groupoid models for the aforementioned systems are models for Z and W, respectively.

Original languageEnglish
Pages (from-to)740-775
Number of pages36
JournalNew York Journal of Mathematics
Volume27
StatePublished - 1 Jan 2021

Keywords

  • Gelfand functor
  • Groupoid models
  • Jiang-Su algebra
  • Razak-Jacelon algebra

ASJC Scopus subject areas

  • Mathematics (all)

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