AF C∗-ALGEBRAS FROM NON-AF GROUPOIDS

Ian Mitscher; Jack Spielberg

doi:10.1090/tran/8723

AF C^∗-ALGEBRAS FROM NON-AF GROUPOIDS

Ian Mitscher, Jack Spielberg

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We construct ample groupoids from certain categories of paths, and prove that their C^∗-algebras coincide with the continued fraction approximately finite dimensional (AF) algebras of Effros and Shen. The proof relies on recent classification results for simple nuclear C^∗-algebras. The groupoids are not principal. This provides examples of Cartan subalgebras in the continued fraction AF algebras that are isomorphic, but not conjugate, to the standard diagonal subalgebras.

Original language	English (US)
Pages (from-to)	7323-7371
Number of pages	49
Journal	Transactions of the American Mathematical Society
Volume	375
Issue number	10
DOIs	https://doi.org/10.1090/tran/8723
State	Published - Oct 1 2022

Keywords

AF algebra
C-algebra
Cartan subalgebra
category of paths
groupoid
higher rank graph

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1090/tran/8723

Cite this

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