Simplicity of crossed products of the actions of totally disconnected locally compact groups on their boundaries

Simplicity of crossed products of the actions of totally disconnected locally compact groups on their boundaries

We prove that if a totally disconnected locally compact group admits a topologically free boundary, then the reduced crossed product of continuous functions on its Furstenberg boundary by the group is simple. We also prove a partial converse of this result.

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Veröffentlicht in:Journal of functional analysis 2025-02, Vol.288 (3), p.110732, Article 110732
1. Verfasser: Arimoto, Ryoya
Format: Artikel
Sprache:eng
Schlagworte:
Furstenberg boundary
Reduced crossed product
Simplicity
Topologically free
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Zusammenfassung:We prove that if a totally disconnected locally compact group admits a topologically free boundary, then the reduced crossed product of continuous functions on its Furstenberg boundary by the group is simple. We also prove a partial converse of this result.
ISSN:0022-1236
DOI:10.1016/j.jfa.2024.110732