The centraliser lattice. New directions in locally compact groups

Hume, David;Stulemeijer, Thierry
(2018) London Mathematical Society. Lecture Note Series — Vol. 447, n° np, p. 267-274 (2018)

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  • Hume, DavidUniversity Oxford
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  • Stulemeijer, ThierryUCLouvain
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Abstract
In this chapter, we review the definition of the centraliser lattice \(\mathcal{LC}(G)\) of a totally disconnected locally compact (tdlc) group, and explain why it is a Boolean algebra. We then study the action of \(G\) on \(\Omega), the associated Stone space of \(\mathcal{LC}(G)\), and prove that under certain hypotheses on \(G\), the action is continuous, minimal, strongly proximal and micro-supported. Moreover, \(\Omega\) satisfies a universal property in the category of profinite \(G\)-spaces that are micro-supported.
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Hume, D., & Stulemeijer, T. (2018). The centraliser lattice. New directions in locally compact groups. London Mathematical Society. Lecture Note Series, 447(np), 267-274. https://hdl.handle.net/2078.5/56624 (Original work published 2018)