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arXiv · 1912.10767

Representation theory of topological full groups of \'etale groupoids and paradoxicality

Vadim Alekseev·Martin Finn-Sell
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Abstract

We provide a unified treatment of several results concerning full groups of ample groupoids and paradoxical decompositions attached to them. This includes a criterion for the full group of an ample groupoid being amenable as well as comparison of its orbit, Koopman and groupoid-left-regular representations. Besides that, we unify several recent results about paradoxicality in semigroups and groupoids, relating embeddings of Thompson's group V into full groups of ample \'etale groupoids.

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Vadim Alekseev, Martin Finn-Sell. 2019-12-23. Representation theory of topological full groups of \'etale groupoids and paradoxicality. https://doi.org/10.1007/s00233-025-10501-w

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