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

Ian Mitscher; Jack Spielberg

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

Operator Algebras 2022-07-06 v4

Authors: Ian Mitscher , Jack Spielberg

Abstract

We construct ample groupoids from certain categories of paths, and prove that their $C^*$ -algebras coincide with the continued fraction 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.

Keywords

c*-algebras c*-algebra cuntz semigroup

Cite

@article{arxiv.2106.14032,
  title  = {AF $C^*$-algebras from non AF groupoids},
  author = {Ian Mitscher and Jack Spielberg},
  journal= {arXiv preprint arXiv:2106.14032},
  year   = {2022}
}

Comments

version 4: final version, to appear in Transactions AMS; minor errors corrected

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