## AF $C^*$-algebras from non-AF groupoids

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- by Ian Mitscher and Jack Spielberg PDF
- Trans. Amer. Math. Soc.
**375**(2022), 7323-7371 Request permission

## 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.## References

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## Additional Information

**Ian Mitscher**- Affiliation: School of Mathematical and Statistical Sciences, Arizona State University, Arizona
- Email: ian.mitscher@gmail.com
**Jack Spielberg**- Affiliation: School of Mathematical and Statistical Sciences, Arizona State University, Arizona
- MR Author ID: 165525
- Email: jack.spielberg@asu.edu
- Received by editor(s): July 20, 2021
- Received by editor(s) in revised form: March 16, 2022, and March 17, 2022
- Published electronically: July 29, 2022
- © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**375**(2022), 7323-7371 - MSC (2020): Primary 46L05; Secondary 46L80, 22A22
- DOI: https://doi.org/10.1090/tran/8723