A groupoid picture of the Elek algebras

Authors

  • Clemens Borys

DOI:

https://doi.org/10.7146/math.scand.a-122419

Abstract

We reformulate a construction by Gábor Elek, which associates $C^{\ast} $-algebras with uniformly recurrent subgroups, in the language of groupoid $C^{\ast} $-algebras. This allows us to simplify several proofs from the original paper and add the converse direction to Elek's characterisation of nuclearity, showing that his sufficient condition is in fact necessary. We furthermore relate our groupoids to the dynamics of the group acting on its uniformly recurrent subgroup.

References

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Published

2021-08-31

How to Cite

Borys, C. (2021). A groupoid picture of the Elek algebras: Array. MATHEMATICA SCANDINAVICA, 127(2), 185–208. https://doi.org/10.7146/math.scand.a-122419

Issue

Section

Articles