## 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 language | English |
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Pages (from-to) | 740-775 |

Number of pages | 36 |

Journal | New York Journal of Mathematics |

Volume | 27 |

State | Published - 1 Jan 2021 |

## Keywords

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

## ASJC Scopus subject areas

- Mathematics (all)

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