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<p>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 <i>V</i> into full groups of ample étale groupoids.</p>

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Representation theory of topological full groups of étale groupoids and paradoxicality

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  • 发表日期：

    2025年1月21日

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  • Vadim Alekseev,
  • Martin Finn-Sell

摘要

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 étale groupoids.