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A groupoid picture of the Elek algebras

A groupoid picture of the Elek algebras

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 …