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- Title
Amenable uniformly recurrent subgroups and lattice embeddings.
- Authors
LE BOUDEC, ADRIEN
- Abstract
We study lattice embeddings for the class of countable groups $\unicode[STIX]{x1D6E4}$ defined by the property that the largest amenable uniformly recurrent subgroup ${\mathcal{A}}_{\unicode[STIX]{x1D6E4}}$ is continuous. When ${\mathcal{A}}_{\unicode[STIX]{x1D6E4}}$ comes from an extremely proximal action and the envelope of ${\mathcal{A}}_{\unicode[STIX]{x1D6E4}}$ is coamenable in $\unicode[STIX]{x1D6E4}$ , we obtain restrictions on the locally compact groups $G$ that contain a copy of $\unicode[STIX]{x1D6E4}$ as a lattice, notably regarding normal subgroups of $G$ , product decompositions of $G$ , and more generally dense mappings from $G$ to a product of locally compact groups.
- Publication
Ergodic Theory & Dynamical Systems, 2021, Vol 41, Issue 5, p1464
- ISSN
0143-3857
- Publication type
Article
- DOI
10.1017/etds.2020.2